Question

A sequence starts:

1, 4, 9, 16 ...
The nth term is n^2
Use this fact to find the nth term of the following sequences:
a)2, 5, 10, 17 ...
b)2, 8, 18, 32 ...

Answer 1

see explanation

Explanation:

Given the sequence

1, 4, 9, 16, ....

has n th term

`a_(n)` = n²

(a)

Given the sequence 2, 5, 10, 17, ......

Note the terms are 1 more than the previous given sequence, thus

`a_(n)` = n² + 1

(b)

Given 2, 8, 18, 32, ......

Note the terms are twice the original given sequence, thus

`a_(n)` = 2n²