Question

, list the first five terms of each sequence, and identify them as arithmetic or geometric.

A(n + 1) = A(n) + 4 for n ≥ 1 and A(1) = −2

Answer 1

Answer: -2, 2, 6, 10, 14

It is an Arithmetic sequence.

Explanation:

Given Recursive formula :
`A(n + 1) = A(n) + 4` , for n ≥ 1 and A(1) = -2.

`A(2)=A(1 + 1) = A(1) + 4=-2+4=2`

`A(3)=A(2 + 1) = A(2) + 4=2+4=6`

`A(4)=A(3 + 1) = A(3) + 4=6+4=10`

`A(5)=A(4 + 1) = A(4) + 4=10+4=14`

Hence, the five terms of given sequence= -2, 2, 6, 10, 14

Since, there is common difference of 4 in two consecutive terms.

Therefore, it is an Arithmetic sequence.