SOLUTION: in a geometric sequence, the fifth term is 48 and the eighth term is 384. find the first term, the common ratio and the formula for the nth term.

Algebra ->  Sequences-and-series -> SOLUTION: in a geometric sequence, the fifth term is 48 and the eighth term is 384. find the first term, the common ratio and the formula for the nth term.      Log On


   

Question 700036: in a geometric sequence, the fifth term is 48 and the eighth term is 384. find the first term, the common ratio and the formula for the nth term.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
a%5B1%5D=first term
r=common ratio
a%5Bn%5D=a%5B1%5D%2Ar%5E%28n-1%29
a%5B8%5D=a%5B1%5D%2Ar%5E7
a%5B4%5D=a%5B1%5D%2Ar%5E4
a%5B8%5D%2Fa%5B4%5D=a%5B1%5D%2Ar%5E7%2F%28a%5B1%5D%2Ar%5E4%29=r%5E3
a%5B8%5D=384 and a%5B4%5D=48
r%5E3=384%2F48=8=2%5E3
highlight%28r=2%29
Substituting r=2 and a%5B4%5D=48 into a%5B4%5D=a%5B1%5D%2Ar%5E4 we get
48=a%5B1%5D%2A2%5E4 --> 48=a%5B1%5D%2A16 --> 48%2F16=a%5B1%5D --> highlight%28a%5B1%5D=3%29
Substituting r=2 and a%5B1%5D=3 into a%5Bn%5D=a%5B1%5D%2Ar%5E%28n-1%29 we get
highlight%28a%5Bn%5D=3%2A2%5E%28n-1%29%29