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

Question

The sum of the first 20 terms common between the series 3 + 7 + 11 + 15 + . . . . . and 1 + 6 + 11 + 16 + . . . . . . is, 4000, 4200, 4220, 4020

MARKS App · Accepted Answer

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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