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The sum of the first 20 terms common between the series 3 + 7 + 11 + 15 +   . . . . . and 1 + 6 + 11 + 16 +   . . . . . . is

Options

  1. A4000
  2. B4200
  3. C4220
  4. D4020

Correct answer

D. 4020

Step-by-step solution

S 1 ≡ 3 ,   7 ,   11 ,   15 , ....... ⇒   c . d = 4 ⇒ d 1 = 4 S 2 ≡ 1 ,   6 ,   11 ,   16 , ....... ⇒   c . d = 5 ⇒ d 2 = 5 ⇒ Every 5 th   term of S 1 and 4 th   term of S 2 will be same ⇒   Terms common to both AP will have a = 11 and d = 20 Hence, S 20 = 20 2 [ ( 2 × 11 ) + ( 20 − 1 ) 20 ] =   10 × 402 =   4020

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