# if the sum of first four terms of an AP IS P AND THE SUM OF FIRST 8 TERMS IF IS Q AND SUM OFfirst 12 terms is r. express 3p+r in terms of q

Sum of n terms of AP is
Sn=$\frac{n}{2}\left[2a+\left(n-1\right)d\right]$
Then,
$S4=\frac{4}{2}\left[2a+3d\right]\phantom{\rule{0ex}{0ex}}P=2\left[2a+3d\right]\phantom{\rule{0ex}{0ex}}P=4a+6d................\left(1\right)$

$S8=\frac{8}{2}\left[2a+7d\right]\phantom{\rule{0ex}{0ex}}Q=4\left[2a+7d\right]\phantom{\rule{0ex}{0ex}}Q=8a+28d......................\left(2\right)$

$S12=\frac{12}{2}\left[2a+11d\right]\phantom{\rule{0ex}{0ex}}R=6\left[2a+11d\right]\phantom{\rule{0ex}{0ex}}R=12a+66d.....................\left(3\right)$

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