The 8 ^ th common term of the series S _ 1 = 3 + 7 + 11 + 15 + 19 +...

Given,

Two A.P's as

$3, 7, 11, 15, . . . </p><p>First term\left({a}_{1}\right) = 3$

Common difference\left({d}_{1}\right)$= 4$

And,

$1, 6, 11, 16, . . .$,

First term\left({a}_{2}\right) = 1$</p><p>Common difference \left({d}_{2}\right)$ = 5$</p><p>Now, common difference of the series of the common terms of the given A.P's is$d = LCM\left({d}_{1}, {d}_{2}\right)$= LCM\left(4, 5\right)$ = 20$</p><p>Now, series of common term is </p><p>$11, 31, 51, 71, . . .

So, ${8}^{th}$ common term appearing in the both the series is

${a}_{8} = 11 + \left(8 - 1\right)d$

$⇒ {a}_{8} = 11 + 7 \times 20 = 151$