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Arithmetic Progression

In an A.P. if...

Question

In an A.P. if $S_{1} = T_{1} + T_{2} + T_{3} + \dots + T_{n}$ (n odd) , $S_{2} = T_{1} + T_{3} + T_{5} + \dots + T_{n}, t h e n S_{1} / S_{2} =$

\frac{2 n}{n + 1}

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\frac{n}{n + 1}

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\frac{n + 1}{2 n}

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\frac{n + 1}{n}

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Solution

The correct option is A $\frac{2 n}{n + 1}$
$S_{1} = \frac{n}{2} [2 a + (n - 1) d]$ ...(1)
$S_{2} = \frac{1}{2} (\frac{n + 1}{2}) [2 a + (\frac{n + 1}{2} - 1) 2 d]$
$= \frac{n + 1}{4} [2 a + (n - 1) d]$ ...(2)
$∴ \frac{S_{1}}{S_{2}} = \frac{2 n}{n + 1} .$

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