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

3, 6, 9, 12,…….. up to 78

$\therefore$Last term $=3+(78-1)3=234$

$5,9,13,17,\mathrm{........}up to 59$

$\therefore$Last term $=5+(59-1)4=237$

Common terms in series is 9, 21, 32,……

If last term is 234 then $234=9+(n-1)12$

$237=12n$

$n=19$ (as we consider integral value of $n$)

So, sum of common terms series $=\frac{19}{2}[2\left(9\right)+(19-1)12]=2223$