Question

Consider the A.Ps 17,21,25,..... and 16,21,26.... Find the sum of first 100 common terms appearing in the two series.

Answer 1

Given,

first common term $a=21$

d of first series $d_1=4$

d of second series $d_2=5$

$\therefore d=20$ [LCM OF 4,5]

$n=100$

$S_n=\frac{100}{2}\left[2\right(21)+(100-1\left)20\right]$

$=50[42+1980]$

$=101100$