The question is :-
find the sum of first 200 terms appearing in both the A P.
1) 17, 21, 25, ………..
2) 16, 21, 26, ………..
If certain nos. appears in both the A.P.s
I searched everywhere, but i only found how to find no. of common terms but not their sum. Even this question has never been asked on this site before.
How to go about solving this question? Please help me.
Thanks.
Best Answer
Well, the first term that appears in both of them is $21$. Since $4$ and $5$ (the forward differences) are coprime, see that the sequences will only be equal every time the sequence increases by $4\times5=20$.
In other words,
$$21+41+61+81+\dots401=\sum_{n=1}^{200}20n+1=200(201)+200=200(202)=40400$$