Question

The sequence

-2, 1, 4, 7, 10,...

is generated recursively by the equations

a1 = -2
an = ________________
A) an = an-1 + 3
B) an = an-1 - 3
C) an = 2an-1 + 5
D) an = -an-1 + 3

Answer 1

A

Explanation:

Note that consecutive terms have a common difference, that is

1 - (- 2) = 4 - 1 = 7 - 4 = 10 - 7 = 3

This indicates that the sequence is arithmetic with d = 3

The next term in the sequence is obtained by adding 3 to the previous term

This can be expressed recursively as

`a_(n)` =
`a_(n-1)` + 3 → with a₁ = - 2