SOLUTION: 20.Please help with this problem https://answers.yahoo.com/question/index?qid=20210419170758AA02SxU

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Question 1179160: 20.Please help with this problem
https://answers.yahoo.com/question/index?qid=20210419170758AA02SxU
Found 2 solutions by MathLover1, mananth:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

If the information given below represents a geometric sequence , find . a%5B3%5D?
a%5B1%5D=3645
a%5B6%5D=15
formula for nth term of a geometric sequence:
a%5Bn%5D=a%5B1%5D%2Ar%5E%28n-1%29
use given to find common ratio r
15=3645%2Ar%5E%286-1%29
15%2F3645=r%5E5
r%5E5=1%2F243
r=root%285%2C1%2F243%29
r=1%2Froot%285%2C243%29
r=1%2Froot%285%2C3%5E5%29
r=1%2F3
a%5Bn%5D=3645%2A%281%2F3%29%5E%28n-1%29
then
a%5B3%5D=3645%2A%281%2F3%29%5E%283-1%29
a%5B3%5D=3645%2A%281%2F3%29%5E2
a%5B3%5D=405



Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Geometric sequence formula
an = a1*r^(n-1)
a1=3645, a6 =15
a1/a6 = 3645/15 = 243
a6= 3645*r^5
3645 = a1
3645*r^5 = a6
divide a1/a6
1/r^5= 243
1/r = 3
r=1/3
a3 = 3645 *(1/3)^2
a3= 3645/9 =405
a2 =1215
a3=405
a4=135
a5=45
a6=15