Question

Find a recursive rule for the nth term of the sequence.

-10, 2, 14, 26, ...

Answer 1

9514 1404 393

Answer:

a[1] = -10

a[n] = 12 + a[n-1]

Explanation:

First differences are ...

• 2 -(-10) = 12
• 14 -2 = 12
• 26 -14 = 12

A constant first difference of 12 means this is an arithmetic sequence. Each term is 12 more than the previous, so the recursive rule is ...

a[1] = -10

a[n] = 12 + a[n-1]