Question

A recursion formula and the initial term of a sequence are given. Write out the first five terms of the sequence. a Subscript font size decreased by 1 1equals6​, a Subscript n plus font size decreased by 1 1equalsminusa Subscript n

Answer 1

6, -6, 6, -6 and 6.

Explanation:

Given the recursion formula for a sequence

`a_(n+1)=-a_n\\$where a_1=6\\`

The first five terms of the sequence are:

`\text{First Term, }a_1=6\\$Second Term, a_2=a_(1+1)=-a_1=-6\\$Third term, a_3=a_(2+1)=-a_2=6\\$Fourth term, a_4=a_(3+1)=-a_3=-6\\$Fifth term, a_5=a_(4+1)=-a_4=6`

Therefore, the first five terms of the sequence:

`a_1,a_2,a_3,a_4,a_5=6, -6, 6, -6$ and 6.`