Question

Determine the fourth term of the sequence defined by the formula:

t1=2a


t2=3a−1


Tn = 2tn−1−3tn−2+1,n ≥ 3




1


−9a+2


-1


−5a+4

Answer 1

B. -9a+2

Explanation:

You are given the sequence

`t_1=2a,\\ \\t_2=3a-1,\dots\\ \\t_n=2t_(n-1)-3t_(n-2)+1,\ n\ge 3`

According to the given rule, find
`t_3,\ n=3`

`t_3=2t_2-3t_1+1=2\cdot (3a-1)-3\cdot 2a+1=6a-2-6a+1=-1`

and
`t_4,\ n=4`

`t_4=2t_3-3t_2+1=2\cdot (-1)-3(3a-1)+1=-2-9a+3+1=-9a+2`