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99 Percentile Qs Bank for JEE MainMathematicsSequences and Series

Let the greatest common divisor of m, n be 1 . If 1 1 7 + 1 7 13 + 1 13 19 + . . . upto 20 terms = m n , then 5 m+2 n=

Options

  1. A325
  2. B330
  3. C342
  4. D337

Correct answer

C. 342

Step-by-step solution

(c) We have, aligned & m n = 1 1 7 + 1 7 13 + 1 13 19 + + 1 [1+(20-1) 6][7+(20-1) 6] & = 1 1 7 + 1 7 13 + 1 13 19 + + 1 115 121 aligned aligned & = 1 6 [ 6 1 7 + 6 7 13 + 6 13 19 + + 6 115 121 ] & = 1 6 [ 7-1 1 7 + 13-7 7 13 + 19-13 13 19 + + 121-115 115 121 ] & = 1 6 [ ( 1 1 - 1 7 )+ ( 1 7 - 1 13 )+ ( 1 13 - 1 19 )+ + ( 1 115 - 1 121 ) ] & = 1 6 [1- 1 121 ]= 1 6 120 121 = 20 121 m=20, n=121 & 5 m+2 n=5 20+2 121=100+242=342 aligned

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