SOLUTION: pls answer it - the first term of arithmetic mean is 1 and the sum of first 9 terms is equal to369 the first and ninth term of gp coincide with first and ninth term of ap find sev

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Question 1043483: pls answer it - the first term of arithmetic mean is 1 and the sum of first 9 terms is equal to369 the first and ninth term of gp coincide with first and ninth term of ap find seventh term of gp
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
WHAT WE KNOW
There is an ap (arithmetic sequence):
a%5B1%5D=1 , a%5B2%5D , a%5B3%5D , ..... , a%5B9%5D .
There is also a gp (geometric sequence):
b%5B1%5D=a%5B1%5D=1 , b%5B2%5D , b%5B3%5D , ..... , b%5B9%5D=b%5B1%5D%2Ar%5E8=1%2Ar%5E8=r%5E8=a%5B9%5D .
a%5B1%5D%2Ba%5B2%5D%2Ba%5B3%5D%2B%22...%22%2Ba%5B9%5D=9%28a%5B1%5D%2Ba%5B9%5D%29%2F2=369
We are looking for b%5B7%5D=b%5B1%5D%2Ar%5E6=1%2Ar%5E6=r%5E6

HOW WE FIND THE ANSWER
9%28a%5B1%5D%2Ba%5B9%5D%29%2F2=369
%28a%5B1%5D%2Ba%5B9%5D%29%2F2=369%2F9
%28a%5B1%5D%2Ba%5B9%5D%29%2F2=41
a%5B1%5D%2Ba%5B9%5D=2%2A41
a%5B1%5D%2Ba%5B9%5D=82
1%2Ba%5B9%5D=82
a%5B9%5D=82-1
a%5B9%5D=81

So, r%5E8=81 ---> r=root%288%2C81%29=root%288%2C3%5E4%29=sqrt%283%29
and b%5B7%5D=%28sqrt%283%29%29%5E6
b%5B7%5D=%283%5E%221+%2F+2%22%29%5E6
b%5B7%5D=3%5E%28%221+%2F+2%22%2A6%29
b%5B7%5D=3%5E3
highlight%28b%5B7%5D=27%29