Question

Sandra wrote the sequence shown:

Answer 1

Answer:

2n^2 + n + 4.

Step-by-step 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.