Question

Let 3, 6, 9, 12, … upto 78 terms and 5, 9, 13, 17, … upto 59 terms be two series. Then, the sum of terms common to both the series is equal to _____.

Answer 1

The correct answer is 2223
Given : 3,6,9,12 ..... upto 78 terms
5,9,13,17 ...... upto 59 terms
Now , last term of first series t78 $= 3+77×3=234$
and last term of second series t59 $= 5+58×4=237$
Now , common difference of common terms = LCM {3,4} = 12
Therefore , First common term is 9 and last common term is 225
So, series will be 9,21,33 ....... 225
$∵ t_n = 225$⇒ 9 + (n-1)12 = 225
⇒ n = 19
∴ Sum of common on terms = $S_n = \frac{19}{2} (9+225) = 2223$