The arithmetic sequence `s = {4, 7, 10, 13, n_(s), n_(6), ….}`. Which step in the sequence involves a 12% increase over the immediately preceding term ?

Options

A. `n_(5)` to `n_(6)`
B. `n_(6)` to `n_(7)`
C. `n_(7)` to `n_(8)`
D. `n_(8)` to `n_(9)`

Answer

D

Explanation

The value of each number in an arithmetic sequence increases by a fixed increment. In this sequence, each term is three greater than the previous one. Use this information to find the values of the other terms of the sequence through `n_(10)`.
`n+(5)=16`
`n_(6)=19`
`n_(7)=22`
`n_(8)=25`
`n_(9)=28`
`n_(10)=31`
You can find the percent increase over the last number in each step by dividing the increase, 3, by the previous number :
`n_(5)` to `n_(6) : (3)/(16)=0.1875`
`n_(6)` to `n_(7) : (3)/(19)=0.1578`
`n_(7)` to `n_(8) : (3)/(22) = 0.1363`
`n_(8)` to `n_(9) : (3)/(25)=0.12`
`n_(9)` to `n_(10) : (3)/(28)=0.1071`
So the percent increase from `n_(8)` to `n_(9)` is 12%