The 8^{{th}{~}} common term of the series S_{1} = 3 + 7 + 11 + 15 + 19 + .. S_{2} = 1 + 6 + 11 + 16 + 21 + .. , is: Sequence & Series (Mathematics)

$S_{1} = 3 + 7 + 11 + 15 + 19 + \ldots.\\$ $\begin{matrix} & a_{1} = 3,d_{1} = 4 \\ & S_{2} = 1 + 6 + 11 + 16 + 21 + \ldots \\ & a_{2} = 1,d_{2} = 5 \end{matrix}\\$ First common term, $a = 11\\$ Common difference, $d = LCM\left( d_{1},d_{2} \right) \\= LCM(4,5) = 20\\$ $8^{\text{th}\text{~}}$ common term . of the series $a_{8} = a + 7d \\= 11 + 7 \times 20 = 151$

Explanation

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