SOLUTION: find the 8th terms of the following series; 6.500 , 9.750 , 14.625 calculate rounding to the third decimal place, and show your workings

Algebra ->  Sequences-and-series -> SOLUTION: find the 8th terms of the following series; 6.500 , 9.750 , 14.625 calculate rounding to the third decimal place, and show your workings      Log On


   

Question 1072565: find the 8th terms of the following series;
6.500 , 9.750 , 14.625
calculate rounding to the third decimal place, and show your workings
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
9.750=6.500%2A1.5 and 14.625=9.750%2A1.5
so this is a geometric sequence
with first term b%5B1%5D=6.500
and common ratio r=1.5 .
For a geometric sequence term number n is
b%5Bn%5D=b%5B1%5D%2Ar%5E%28n-1%29
and the sum of the first n terms is
S%5Bn%5D=n%28r%5En-1%29%2F%28r-1%29
In this case,
b%5B8%5D=6.500%2A1.5%5E%288-1%29=6.500%2A1.5%5E7=6.5%2A17.0859375=111.05859375
and
S%5B8%5D=6.500%281.5%5E8-1%29%2F%281.5-1%29=6.500%2A25.62890625%2F0.5=333.17578125 .
Rounding to the third decimal place,
b%5B8%5D=111.059 and S%5B8%5D=333.176 .