The sum of the first 5 terms of a geometric progression is the same as the sum of the first 7 terms of the same progression. If the sum of the first 9 terms is 24, then the 4th term of the progression is

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Accepted Answer

S5​=S7​ implies the 6th and 7th terms cancel each other, so r=−1. Then S9​=a⋅1−(−1)1−(−1)9​=a=24. The 4th term = a⋅r3=24⋅(−1)=−24.