The first two terms of a geometric progression add up to 12 . The sum of the third and the fourth terms is 48 . If the terms of the geometric progress - Mathematics MCQ AIEEE 2026 | ExamTest.live

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The first two terms of a geometric progression add up to 12 . The sum of the third and the fourth terms is 48 . If the terms of the geometric progression are alternately positive and negative, then the first term is:

Solution & Step-by-step Explanation

Let the GP be a, a r, a r^{2}, a r^{3}, \dots .Given a + a r = 12 ⟹ a (1 + r) = 12 ... (1)And a r^{2} + a r^{3} = 48 ⟹ a r^{2} (1 + r) = 48 ... (2)Dividing (2) by (1): \frac{a r ^{2} ( 1 + r )}{a ( 1 + r )} = \frac{48}{12} ⟹ r^{2} = 4 ⟹ r = \pm 2 .Since terms are alternately positive and negative, r must be negative. So r = - 2 .Substitute r = - 2 in (1): a (1 - 2) = 12 ⟹ - a = 12 ⟹ a = - 12 .

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The first two terms of a geometric progression add up to 12 . The sum of the third and the fourth terms is 48 . If the terms of the geometric progression are alternately positive and negative, then the first term is:

- 4

- 12

12

4

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