A recursion formula and the initial term(s) of a sequence are given. Write out the first five terms of the sequence.
-$a _ { 1 } = 1 , a _ { n + 1 } = a _ { n } + 5$
A) 6, 11, 16, 21, 26
B) 1, 6, 11, 16, 21
C) 1, 6, 11, 16, 21, 26
D) 1, 5, 25, 125, 625, 3125

Question

Quizplus · Accepted Answer

We can plug in the value of n to find the first few terms of the sequence:
$a_1 = 1$
$a_2 = a_1 + 5 = 6$
$a_3 = a_2 + 5 = 11$
$a_4 = a_3 + 5 = 16$
$a_5 = a_4 + 5 = 21$
Therefore, the first five terms of the sequence are 1, 6, 11, 16, 21, which is option B. Option A is incorrect because it starts with 6 instead of 1. Option C is incorrect because it includes an extra term (26). Option D is unrelated to the given recursion formula.

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A Recursion Formula and the Initial Term(s) of a Sequence $a _ { 1 } = 1 , a _ { n + 1 } = a _ { n } + 5$