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A geometric progression has an even number of terms. If the total of all its terms is five times the sum of the terms in the odd positions, then the common ratio is

1. 5
2. 1
3. 4
4. 3

Correct answer: 4

Solution

For a GP, the even-position terms sum to r times the odd-position sum, so total = (1+r)*S_odd. Given total = 5*S_odd, we get 1+r = 5, hence r = 4.

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