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JEE Main 2026 Mathematics question

MathematicsSequence and SeriesJEE Main 2026

The sum of the first ten terms of an A.P. is 160 and the sum of the first two terms of a G.P. is 8. If the first term of the A.P. is equal to the common ratio of the G.P. and the first term of the G.P. is equal to common difference of the A.P., then the sum of all possible values of the first term of the G.P. is:

Answer: (A)

Solution

Let the G.P. have first term g and ratio r. Then the A.P. has first term r and difference g: 5(2r+9g)=160 gives 2r+9g=32, and

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Question ID VK-015640