Question

The first term of an arithmetic progression is `1` and the sum of the first nine terms equal to `369`. The first and the ninth term of a geometric progression coincide with the first and the ninth term of the arithmetic progression. Find the seventh term of the geometric progression.

Answer 1

`a=1`
Sum of 9 terms=369
=`9/2*(2*1+((9-1)*d)=369` `4d+1=41`
`d=10`
9th term of A.P=`a+8d=1+80=81`
1st term of G.P=A=1
9th term of G.P=`AR^8=81`
On solving, `R^8=81`
`R=sqrt(3)`
7th term of G.P=`AR^(7-1)=(sqrt3)^6=27`