Question

The first four terms in a sequence, and the rules that define

them, are shown below.
a1 =4
a2 = 2a1 + 3
a3 = 2a2 + 3
a4 = 2a3 + 3
What is the value of a4, the fourth term shown in the
sequence above?
A 35
B 41
C 25
D 53

Answer 1

Answer: D. 53
`a_(4)=53`

Explanation:

`a_(1)=4\\a_(2)=2(a_(1))+3\\a_(3)=2(a_(2))+3\\a_(4)=2(a_(3))+3`

`a_(2)=2(a_(1))+3\\a_(2)=2(4)+3\\a_(2)=8+3\\a_(2)=11`

`a_(3)=2(a_(2))+3\\a_(3)=2(11)+3\\a_(3)=22+3\\a_(3)=25`

`a_(4)=2(a_(3))+3\\a_(4)=2(25)+3\\a_(4)=50+3\\a_(4)=53`