SOLUTION: I am having trouble with this problem. I am not supposed to have decimal answers. Find the 19th term of 3/8, 1/2, 5/8 Thank you in advance.

Algebra ->  Sequences-and-series -> SOLUTION: I am having trouble with this problem. I am not supposed to have decimal answers. Find the 19th term of 3/8, 1/2, 5/8 Thank you in advance.      Log On


   

Question 1115601: I am having trouble with this problem. I am not supposed to have decimal answers.
Find the 19th term of 3/8, 1/2, 5/8
Thank you in advance.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

to find the 19th term of 3%2F8, 1%2F2, 5%2F8 or 3%2F8, 4%2F8, 5%2F8
first find common difference d
d=1%2F2-3%2F8=4%2F8-3%2F8=1%2F8 or
d=5%2F8+-1%2F2=5%2F8-4%2F8=1%2F8
so, d=1%2F8
since first term a%5B1%5D=3%2F8, 19th term =>n=19
use formula
a%5Bn%5D=a%5B1%5D%2B%28n-1%29d
a%5B19%5D=3%2F8%2B%2819-1%29%281%2F8%29
a%5B19%5D=3%2F8%2B18%2F8
a%5B19%5D=21%2F8
your sequence is:
3%2F8, 4%2F8, 5%2F8 ,6%2F8,7%2F8,8%2F8,9%2F8,10%2F8,11%2F8,12%2F8,13%2F8,14%2F8,15%2F8,16%2F8,17%2F8,18%2F8,19%2F8,20%2F8,21%2F8,...
or, simplified
3%2F8, 1%2F2, 5%2F8 ,3%2F4,7%2F8,1,9%2F8,5%2F4,11%2F8,3%2F2,13%2F8,7%2F4,15%2F8,2,17%2F8,9%2F4,19%2F8,5%2F2,21%2F8,...