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Let a 1 , a 2 , … … , a n be in A.P. If a 5 = 2 a 7 and a 11 = 18 , then 12 1 a 10 + a 11 + 1 a 11 + a 12 + … . . 1 a 17 + a 18 is equal to _____ .

Correct answer

0

Step-by-step solution

Let the common difference of an A.P. be d , then 2 a 7 = a 5 (given) ⇒ 2 a 1 + 6 d = a 1 + 4 d ⇒ a 1 + 8 d = 0               … 1 And, a 11 = 18 ⇒ a 1 + 10 d = 18                   … 2 Solving 1 and 2 , we get a 1 = - 72 , d = 9 So, a 18 = a 1 + 17 d = - 72 + 153 = 81 a 10 = a 1 + 9 d = 9 Now, 12 1 a 10 + a 11 + 1 a 11 + a 12 + … . . 1 a 17 + a 18 = 12 a 11 - a 10   d + a 12 - a 11   d + &#82

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