Question

Write a recursive formula for the following arithmetic sequence.

16,13,10,7

a1=
a(n)= blank for n >_ 2

Answer 1

a1 = 16

a(n) = a(n-1) -3 for n ≥ 2

Explanation:

You want a recursive formula for the arithmetic sequence 16, 13, 10, 7, ....

Arithmetic sequence

The given sequence has a first term of 16. The common difference is ...

13 -16 = -3

Each successive term is found by adding this difference to the one before. That describes the relation expressed by the recursive formula.

`\begin{cases}a_1=16\\a_n=a_(n-1)-3&\text{for $n\ge2$}\end{cases}`