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

27

Explanation

`369=9/2[2+(9-1)d]`
`rArr82=2+8d`
`rArrd=10`
Now, `ar^(8)=a+8d`
`rArr1xxr^(8)=1+8xx10`
`rArrr^(8)=81`
`rArrr=sqrt3`
`rArrar^((7-1)=1xx(sqrt3)^(6)=27`