Question

What is the recursive formula for this sequence?

A)a(1) = 1 and a (n-1) + 5
B)a(1) = 6 and a (n-1) + 5
C)a(1) = 6 and a(n) = a (1) + 6
D)a(1) = 1 and a (n) = a(6) + 1​

Answer 1

B)
`a_1=6` and
`a_n=a_(n-1)+5`

Explanation:

The given sequence is 6, 11, 16, 21,...

The common difference is d=11-6=5

The first term in the sequence is
`a_1=6`

The recursive formula for an arithmetic sequence is given as:

`a_n=a_(n-1)+d`

Substitute the above information to get:

`a_n=a_(n-1)+5,\:\:a_1=6`