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

Answer:

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

Step-by-step 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:

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