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

Answer:

B) $a_1=6$ and $a_n=a_{n-1}+5$

Step-by-step 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:

$a_n=a_{n-1}+5,\:\:a_1=6$