SOLUTION: Can someone please help me with this problem: Find the indicated term of the geometric sequence. {{{a[1]=1/3}}}, {{{r=1/2}}}; Find the 8th term.

Algebra ->  Sequences-and-series -> SOLUTION: Can someone please help me with this problem: Find the indicated term of the geometric sequence. {{{a[1]=1/3}}}, {{{r=1/2}}}; Find the 8th term.      Log On


   

Question 203569: Can someone please help me with this problem:
Find the indicated term of the geometric
sequence.
a%5B1%5D=1%2F3, r=1%2F2; Find the 8th term.
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
Can someone please help me with this problem:
Find the indicated term of the geometric
sequence.
a%5B1%5D=1%2F3, r=1%2F2; Find the 8th term.
 
The formula for the nth term of a geometric sequence is: 

a%5Bn%5D=a%5B1%5Dr%5E%28n-1%29

Substitute n=%288%29, a%5B1%5D=%281%2F3%29, r=%281%2F2%29

a%5B8%5D=%281%2F3%29%281%2F2%29%5E%28%288%29-1%29

a%5B8%5D=%281%2F3%29%281%2F2%29%5E7

a%5B8%5D=%281%2F3%29%281%2F2%5E7%29

a%5B8%5D=%281%2F3%29%281%2F2%5E7%29

a%5B8%5D=%281%2F3%29%281%2F128%29

a%5B8%5D=1%2F%283%2A128%29

a%5B8%5D=1%2F384

Check:

1st term = 1%2F3
2nd term = 1st term times the ratio, 1%2F2, = %281%2F3%29%2A%281%2F2%29=1%2F6
3rd term = 2nd term times the ratio, 1%2F2, = %281%2F6%29%2A%281%2F2%29=1%2F12
4th term = 3rd term times the ratio, 1%2F2, = %281%2F12%29%2A%281%2F2%29=1%2F24
5th term = 4th term times the ratio, 1%2F2, = %281%2F24%29%2A%281%2F2%29=1%2F48
6th term = 5th term times the ratio, 1%2F2, = %281%2F48%29%2A%281%2F2%29=1%2F96
7th term = 6th term times the ratio, 1%2F2, = %281%2F96%29%2A%281%2F2%29=1%2F192
8th term = 7th term times the ratio, 1%2F2, = %281%2F192%29%2A%281%2F2%29=1%2F384

Edwin