Quadratic Sequences: The Nth Term of a Quadratic Number Sequence

The first differences are 7, 11, 15, 19.

The second differences are 4.

Half of 4 is 2, so the first term of the sequence is 2n^2.

If you subtract 2n^2 from the sequence you get 0,1,2,3,4 which has the nth term of n - 1

Therefore your final answer will be 2n^2 + n - 1

The first differences are 6,8,10,12,14. The second difference is 2. Therefore half of 2 is 1 so the first term is n^2. Subtract this from the sequence gives 5,8,11,14,17. The nth term of this sequence is 3n + 2. So the final formula for this sequence is n^2 + 3n + 2.

The first differences are 10, 14, 18, and the second differences are all 4, so the sequence must be quadratic.

Half of 4 gives 2, so the first term of the nth term is 2n^2.

Subtracting 2n^2 from the sequence gives 1, 5, 9, 13 which has nth term of 4n -3.

So the final nth term is 2n^2 + 4n - 3.

The first differences are 10, 14, 18, 22 and the second differences are 4. Therefore the first term is 2n^2 as half os 4 gives 2.

Subtracting 2n^2 from the sequence gives 1, 5, 9, 13, 17 which has nth term of 4n -3.

Putting all this together givers 2n^2 + 4n - 3.

The fist differences are 4, 8, 12, and the second difference are 4.

Since the second difference are 4, then the first term of the nth term is 2n^2 (Half 4).

Subtracting 2n^2 from the sequence gives 9, 7, 5, 3, which has nth term -2n + 11.

So the final answer is 2n^2 - 2n + 11.

The first differences are 4,6,8,10, and the second differences are 2 giving the first term of n^2.

Subtracting n^2 from this sequence gives 5,6,7,8,9 which has nth term of n + 4.

So the nth term of this quadratic sequence is n^2 + n + 4.

The first differences are 3, 5, 7 and the second difference are 2.

Since the second differences are 2, then half of 2 is 1, so the first tem of the sequence is n^2.

Subtracting n^2 from this squences gives 1,1,1,1.

So the nth term of this quadratic sequence is n^2 + 1.

The first differences are 15,23,31,39, and the second differences are 8.

Halving 8 gives 4, so the first term of the formula is 4n^2

Now subtract 4n^2 from this sequence to give -1,2,5,8,11, and the nth term of this sequence is 3n – 4.

So the nth term of the quadratic sequence is 4n^2 + 3n – 4.

The first differences are 14, 20, 26, 32 and 38, and so the second differences are all 6.

Halving 6 gives 3, so the first term of the sequence is 3n^2.

Subtracting 3n^2 from the sequences gives 3,8,13,18,23 which has the nth term 5n-2.

Therefore, the formula for this sequence is 3n^2 + 5n - 2.

The first differences are 3,7,11,15,19 and the second differences are 4.

Halving 4 gives 2, so the first term of the formula is 2n^2.

Now subtract 2n^2 from this sequence to give -9,-12,-15,-18, -21, -24 and the nth term of this sequence is -3n -6.

So the nth term of the quadratic sequence is 2n^2 – 3n – 6.

The first differences are 0, 2, 4, 6, and the second diffferences are all 2.

Since half of 2 is 1, then the first term of the quadratic nth term is n^2.

Next, subtract n^2 from the sequence to give -9,-12,-15,-18,-21 which has nth term -3n - 6.

So the nth term will be n^2 -3n - 6.

The first difference of the sequence are 8, 10, 12, 24.

The second differences of the sequences are 2, therefore since half of 2 is 1 then the first term of the sequence is n^2.

Subtracting n^2 from the given sequence gives, 7,12,17,22,27. The nth term of this linear sequence is 5n + 2.

So if you put the three-term together, this quadratic sequence has the nth term n^2 + 5n + 2.

First work out the first differences, these are 5, 9, 13, 17.

Next, find the second differences, these are all 4.

So since half of 4 is 2, then the first term is 2n^2.

Subtracting 2n^2 from the sequence gives 1, 0, -1, -2, -3 which has nth term of -n + 2.

So the nth term of this quadratic sequence is n^2 -n + 2.

The first differences are -5, -11, -17, and so the second differences are all 6.

Halving 6 gives 3, so the first term of the sequence is 3n^2.

Subtracting 3n^2 from the sequences gives -7,-11,-15,-19 which has the nth term -4n-3.

Therefore, the formula for this sequence is 3n^2 -4n - 3.

The first differences are 8,10,12,14,16,18, and the second differences are 2, so the first term will be n^2.

Subtracting n^2 from the sequence gives 7,12,17,22,27,32,37 which has nth term of 5n + 2.

So the final answer is n^2 + 5n + 2.

These numbers are 8 more than the square number sequence, so the nth term is n^2 + 8.

The first difference are 3, 5, 7 and 9. The second differences 2, so the first term is n^2 (since half of 2 is 1).

Subtracting n^2 from the sequence gives 3.

So the nth term of this quadratic sequence is n^2 + 3.

The first differences are 4, 12, 20.

The second differences are 8.

Therefore, since 1/2 of 8 = 4, then the first term of the quadratic sequence is 4n^2.

Subtract 4n^2 from the sequence gives 1, -7, -15, -23 and the nth term of the linear sequence is -8n + 9.

Hence the nth term of this quadratic sequence is 4n^2 -8n + 9.

The first differences are 8,10,12,14,16,18 and the second differences are 2.

Since half of 2 is 1, then the first term of the nth term is n^2.

Subtracting n^2 from the sequence gives 7,12,17,22,27,32,37 which has a nth term of 5n + 2.

So putting these together gives a nth term of the quadratic sequence of n^2 + 5n + 2.

The first differences are 8, 12, 16, so the next difference will be 20 as the first differences are increasing by 4. Therefore the next term is 40 + 20 = 60.

First find the first differences to give 3, 5, 7, 9 and therefore the second differences are 2.

This means the first term will be n^2 as half of 2 is 1.

Subtracting n^2 from the sequence gives 3.

So the final formula for the sequence is n^2 + 3.

First, work out the first differences; these are 8, 14, 20.

Next, find the second differences, these are all 6.

So since half of 6 is 3, then the first term is 3n^2.

Subtracting 3n^2 from the sequence gives 0, -1, -2, -3 which has nth term of -n + 1.

So the nth term of this quadratic sequence is 3n^2 -n + 1.

This sequence is 4 times bigger than the square number sequence, so the nth term is 4n^2.

The first differences are 3, 5, 7, 9 and the second diffferences are all 2.

Since half of 2 is 1, then the first term of the quadratic nth term is n^2.

Next subtract n^2 from the sequence to give 3 for each term.

So the nth term will be n^2 + 3.

The first differences in the sequence are 1, 3, 5, 7, 9, 11 and the second differences are all 2.

Halving that equals 1, so the first term of the sequence is n^2.

Subtracting n^2 from the sequence gives -6, -8, -10, -12, -14, -16, -18, which has nth term -2n - 4.

So the final answer is n^2 -2n - 4.

The fist differences are 15, 23, 31, and the second difference are 8.

Since the second difference are 8, then the first term of the nth term is 4n^2 (Half of 8).

Subtracting 4n^2 from the sequence gives -2, 1, 4, 7, which has nth term 3n -5.

So the final answer is 4n^2 + 3n -5.

The first differences are 6 8,10 and the second differences are 2.

The first term of the sequence is therefore n^2 (since half of 2 is 1).

Subtracting n^2 from the sequecne gives 2, 5, 8, 11 which has the nth term of 3n - 1.

So putting the 3 terms together gives a final answer of n^2 + 3n - 1.

Make n^2 + 5 = 174.

Subtract 5 from both sides to give n^2 = 169.

Then square root both sides to give n = 13.

174 is the 13th term in the sequence, so yes.

The first differences are 3,5,7,9,11 and the second differences are 2.

The first term of the sequence is, therefore, n^2 (since half of 2 is 1).

Subtracting n^2 from the sequence gives 6.

So putting these 2 terms together gives a final answer of n^2 + 6.

The first differences are 8, 14, 20 and the second difference is 6.

Since half of 6 gives 3, the first term of the sequence is 3n^2.

Subtracting 3n^2 from this sequence gives -1, -2, -3, -4, which has a nth term of -n.

Therefore putting this together gives an answer of 3n^2 -n.

The first differences are 15, 23, 31, and so the second differences are all 8.

Halving 8 gives 4, so the first term of the sequence is 4n^2.

Subtracting 4n^2 from the sequences gives -2, 1, 4, 7 which has the nth term 3n - 5

Therefore, the formula for this sequence is 4n^2 + 3n - 5.

Assuming that the sequence is quadratic the first difference are 11 and 13. So the first differences are increasing by 2 each times.

So the fourth term will be 50 + 15 = 65.

The fifth term will be 65 + 17 = 82.

The sixth term will be 82 + 19 which is 101.

The first differences are 3, 5, 7, 9, 11 and the second differences are all 2, so the sequence must be quadratic.

Half of 2 gives 1, so the first term of the nth term is n^2.

Subtracting n^2 from the sequence gives -5.

So putting both terms together gives n^2 -5.

The first differences are 10, 16, 22, and the second difference are 6 meaning that the sequence is quadratic and the first term being 3n^2.

Subtracting 3n^2 from the sequence gives -2,-1,0,1 which has nth term n - 3.

So putting these terms together gives a final answer of 3n^2 + n - 3.

The first differences are 2,4,6,8,10,12, and the second differences are 2.

So the first term of the sequence is n^2.

Subtracting n^2 from the sequence gives 3,2,1,0,-1,-2,-3 which has nth term -n + 4.

So the nth term is n^2 - n + 4.

The first differences are 3, 5, 7 and 9, and the second differences are 2.

Therefore the first term will be n^2 (half of 2 is 1).

Subtracting n^2 from the sequences gives 3.

So the final answer is n^2 + 3.

This is your square number sequence starting at 0 instead of 1.

Therefore the nth term will be (n-1)^2.

The fist differences are 3, 5, 7, 9, and the second difference are 2.

Since the second differences are 2, then the first term of the nth term is n^2 (Half 2).

Subtracting n^2 from the sequence gives 5.

So the final answer is n^2 + 5.

The first differences are 3,5,7,9,11, and the second differences are 2.

Therefore the first term in the quadratic sequence is n^2.

Subtracting n^2 from the sequence gives -4.

So the final answer of this sequence is n^2 -4.

(Just subtract 4 from your square number sequence).

The first differences are 2,3,4,5 and the second differences are 1.

Therefore the first term in the quadratic sequence is 0.5n^2.

Subtracting 0.5n^2 from the sequence gives 0.5, 1, 1.5, 2, 2.5, and the nth term of this linear sequence is 0.5n.

So the final answer of this sequence is 0.5n^2 + 0.5n.

These are the even square numbers.

2 squared is 4.

4 squared is 16.

6 squared is 36.

8 squared is 64.

10 squared is 100.

So the next term in the sequence will be 12 squared which is 144, then the next one 14 squared which 196 etc.

First look for the nth term of the numerators of each fraction (1,4,9,16). Since these are square numbers then the nth term of this sequence is n^2.

The denominators of each fraction are 2,3,4,5, and this is a linear sequence with nth term n + 1.

So putting these together the nth term of this fractional number sequence is n^2/(n+1).

The first differences are 6,8,10,12, and the second differences are 2.

Since half of 2 is 1, then the first term of the nth term is n^2.

Subtracting n^2 from the sequence gives 3,6,9,12,15 which has a nth term of 3n.

So putting these together gives a nth term of the quadratic sequence of n^2 + 3n.

The first differences are 5, 11, 17, 23, 29, and the second differences are 6.

Halving 6 gives 3, so the first term will be 3n^2.

Subtracting 3n^2 from the sequence gives -7, -11, -15, -19, -23, -27, which has nth term -4n -3.

So the final answer will be 3n^2 -4n - 3.

First find the first differences to give 12, 22, 32, and therefore the second differences are 10.

This means the first term will be 5n^2 as half of 10 is 5.

Subtracting 5n^2 from the sequence gives -3, -6, -9, -12, which has nth term -3n.

So the final formula for the sequence is 5n^2 - 3n.

These terms in the sequence are 3 higher than the square number nth term, so the nth term is n^2 + 3

Assuming the sequence is quadratic then the first differences are -6, k + 5, and -23 - k.

The second differences are k + 11 and -2k and -28.

Since the second differences are the same of a quadratic sequence then k + 11 = -2k - 28.

This gives 3k = -39, and k = -13.

The fist differences are 1, 2, 3, 4 and the second difference are 1.

Since the second differences are 1, then the first term of the nth term is 0.5n^2 (Half of 1).

Subtracting 0.5n^2 from the sequence gives 0.5,0,-0.5,-1,-1.5 which has nth term -0.5n + 1.

So the final answer is 0.5n^2 - 0.5n + 1.

The first differences are 4, 8, 12, and the second differences are 4.

Since half of 4 is 2 then the first term of the nth term is 2n^2.

Subtracting 2n^2 from this sequence gives 3, 1, -1, -3 which has nth term of -2n + 5.

So putting this together gives 2n^2 -2n + 5.

To work this out the numbers 1,2 and 3 need to be substituted into the nth term.

So the first term is 1^2 + 20 = 21.

The second term is 2^2 + 20 = 24.

The third term is 3^2 + 20 = 29.

So the first three terms are 21,24,29.

First find the first differences to give 8, 12, 16, and therefore the second differences are 4.

This means the first term will be 2n^2 as half of 4 is 2.

Subtracting 2n^2 from the sequence gives 6, 8, 10, 12, which has nth term of 2n + 4.

So the final formula for the sequence is 2n^2 + 2n + 4.

First work out the first differences, these are 14, 20, 26, 32, 38

Next find the second differences, these are all 6.

So since half of 6 is 3, then the first term is 3n^2.

Subtracting 3n^2 from the sequence gives 7, 12, 17, 22, 27 which has nth term of 5n + 2.

So the nth term of this quadratic sequence is 3n^2 + 5n + 2.

The first differences are 2,4,6,8, and the second differences are 2.

Therefore, the first term will be n^2.

Subtracting n^2 from the sequence gives 0,-1,-2,-3,-4 which has nth term of -n + 1.

So the final answer is n^2 - n + 1.

The fist differences are 6, 10, 14, 18 and the second difference are 4.

Since the second differences are 4, then the first term of the nth term is 2n^2 (Half 4).

Subtracting 2n^2 from the sequence gives -10.

So the final answer is 2n^2 - 10.

The first differences are 4,5,6, and the second differences are 1, so the first term will be 0.5n^2.

Subtracting 0.5n^2 from the sequence gives 2.5,5,7.5,10 which has nth term of 2.5n.

So the final answer is 0.5n^2 + 2.5n.