The first series goes as follows: 46,54,62,70,78,86,94,102,.... The second series goes as follows: 98,102,106,110,... The first common term is 102 (first term of the common terms) and the common difference between them will be hcf(4,8)=8 ⇒ The required sequence is 102,110,118,..... (last term should be less than 468 (100th term of second series)) ⇒102+(n−1)(8)≤498 ⇒n is less than or equal to 50.5⇒n=50 Using the summation of A.P. formula: Required sum