A recursion formula and the initial term(s) of a sequence are given. Write out the first five terms of the sequence.
-$$a _ { 1 } = 1 , a _ { 2 } = 4 , a _ { n + 2 } = a _ { n + 1 } + a _ { n }$$
A) $1,4,5,9,14$
B) $1,4,5,6,7$
C) $1,4,5,10,15$
D) $1,1,2,3,5$

Question

Quizplus · Accepted Answer

The sequence starts with $a_1 = 1$ and $a_2 = 4$. Each subsequent term is the sum of the two preceding terms. So, $a_3 = a_2 + a_1 = 4 + 1 = 5$, $a_4 = a_3 + a_2 = 5 + 4 = 9$, and $a_5 = a_4 + a_3 = 9 + 5 = 14$. Therefore, the first five terms are $1, 4, 5, 9, 14$.

A Recursion Formula and the Initial Term(s) of a Sequence a1=1,a2=4,an+2=an+1+ana _ { 1 } = 1 , a _ { 2 } = 4 , a _ { n + 2 } = a _ { n + 1 } + a _ { n }a1​=1,a2​=4,an+2​=an+1​+an​

A Recursion Formula and the Initial Term(s) of a Sequence $a _ { 1 } = 1 , a _ { 2 } = 4 , a _ { n + 2 } = a _ { n + 1 } + a _ { n }$