Question

Sandra wrote the sequence shown:

7, 14, 25, 40, 59
Complete each of the 2 activities for this Task.
Activity 1 of 2
What explicit expression can be used to find the nth term of this sequence?

Answer 1

2n^2 + n + 4.

Explanation:

7, 14, 25, 40, 59

The differences are 7, 11, 15, 19 which is arithmetic sequence so the given sequence is quadratic.

Compile a table:

n 1 2 3 4 5

term 7 14 25 40 59

Diff: 7 11 15 19

Diff: 4 4 4 - this indicates that first part is 2n^2.

2n^2 2 8 18 32 50

term-2n^2 5 6 7 8 9

- the nth term for the last sequence is 5+ (n - 1)d =

= 5 + (n - 1)* 1

= n + 4.

So nth term for the original sequence is 2n^2 + n + 4.