SOLUTION: 1, 4, 7, 10, ... What is the 100th number in this sequence?

Algebra ->  Sequences-and-series -> SOLUTION: 1, 4, 7, 10, ... What is the 100th number in this sequence?      Log On


   

Question 341734: 1, 4, 7, 10, ... What is the 100th number in this sequence?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

1, 4, 7, 10, ... What is the 100th number in this sequence?

This sequence has a common difference d=3 because

4-1=7-4=10-7=3

So it is an arithmetic sequence with first term = a%5B1%5D=1
and d=3

The formula for the nth term is

a%5Bn%5D%22%22=%22%22a%5B1%5D%2B%28n-1%29d

Substitute n=100, a%5B1%5D=1, d=3

a%5B100%5D=%22%221%2B%28100-1%29%283%29

a%5B100%5D=%22%221%2B%2899%29%283%29

a%5B100%5D=%22%221%2B297

a%5B100%5D=%22%22298

Edwin