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Let a 1 , a 2 , a 3 , … . be a GP of increasing positive numbers. If the product of fourth and sixth terms is 9 and the sum of fifth and seventh terms is 24 , then a 1 a 9 + a 2 a 4 a 9 + a 5 + a 7 is equal to

Correct answer

0

Step-by-step solution

Given, a 1 , a 2 , a 3 , … . be a GP of increasing positive numbers, And the product of fourth and sixth terms is 9 So, a 4 · a 6 = 9 ⇒ a 5 2 = 9 ⇒ a 5 = 3 Also given the sum of fifth and seventh terms is 24 , So, a 5 + a 7 = 24 ⇒ a 5 + a 5 r 2 = 24 ⇒ 1 + r 2 = 8 ⇒ r = 7 Now using a 5 = 3 ⇒ a 1 r 4 = 3 ⇒ a 1 = 3 r 4 = 3 49 Then, a 1 a 9 + a 2 a 4 a 9 + a 5 + a 7 = 3 49 × 3 49 × 7 8 + 3 49 × 7 × 3 49 × 7 3 × 3 49 × 7 8 + 3 49 &#2

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