A recursion formula and the initial term(s) of a sequence are given. Write out the first five terms of the sequence.
-$$a _ { 1 } = 1 , a _ { n + 1 } = a _ { n } + 6$$
A) $7,13,19,25,31$
B) $1,7,13,19,25$
C) $1,7,13,19,25,31$
D) $1,6,36,216,1296,7776$

Question

Quizplus · Accepted Answer

We can use the recursion formula to find the first few terms of the sequence: 
$$a_2 = a_1 + 6 = 1 + 6 = 7$$
$$a_3 = a_2 + 6 = 7 + 6 = 13$$
$$a_4 = a_3 + 6 = 13 + 6 = 19$$
$$a_5 = a_4 + 6 = 19 + 6 = 25$$
Therefore, the first five terms of the sequence are 1, 7, 13, 19, and 25, which corresponds to choice B.

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A Recursion Formula and the Initial Term(s) of a Sequence $a _ { 1 } = 1 , a _ { n + 1 } = a _ { n } + 6$