# The fourth term of a geometric series is 30 . The 9th term is 960 . Find the sum of the first 9 terms

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justaguide | Certified Educator

The fourth term of the geometric series is 30. The 9th term is 960. If the first term of the series is a and the common ratio is r, the nth term is `T_n = a*r^(n - 1)`

30 = a*r^3 and 960 = a*r^8

960/30 = r^5

=> r = 2

a = 30/8 = 15/4

The sum of the first n terms of the series is `a*(r^n - 1)/(r - 1)` . The sum of the first 9 terms is (15/4)*(2^9 - 1) = 7665/4

**The sum of the first 9 terms is 7665/4**