Question

What is the nth term of -4,-3,0,5,12,21,32?

Answer 1

The first set of differences is   1,3,5,7,9,11

second set of difference = 2 so this is a quadratic sequence  with first term n^2

subtract n^2 from the sequence:-

-4  -  3    0     5

1      4     9    16

-5   -7    -9     -11  

This last series is an AP with nth term = - 5-2(n - 1)

so nth term  for original series is n^2 - 5 - 2(n - 1)

= n^2  - 2n  - 3  answer

Answer 2

This question is based on the arithmetic progression. The nth term of the -4,-3,0,5,12,21,32  is  $\bold{n^2 - 5 - 2(n - 1)}$.

Given:

Sequence is -4,-3,0,5,12,21,32.

We need to determined the nth term of the given sequence.

According to the question,

The first set of differences is 1,3,5,7,9,11 .  

Now, second set of difference = 2.

Hence, this is a quadratic sequence with first term $\bold{n^2}$.

Now, subtracting $\bold{n^2}$  from the sequence.

We get,

-4  -  3    0     5

1      4     9    16

-5   -7    -9     -11  

This last series is an arithmetic progression with nth term = - 5 - 2 (n - 1)

Therefore, the  nth term  for original series is  $\bold{n^2 - 5 - 2(n - 1)}$.

For more details, prefer this link:

https://brainly.com/question/16935540