# What is the formula used when in.a series the terms have common difference in AP...??!

$BelowaretheformulasusedifaseriesisinA.P.,\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}Tofindthe{n}^{th}termofanAP\left({T}_{n}\right)=a+\left(n-1\right)d\phantom{\rule{0ex}{0ex}}Tofindsumofntermsinaseries=\frac{n}{2}\left[2a+\left(n-1\right)d\right]\phantom{\rule{0ex}{0ex}}BelowaretheformulasusedifthedifferenceinaseriesformsanA.P.\phantom{\rule{0ex}{0ex}}forexample=1,3,6,10,15,21,28,36inthisseriesthedifferenceis2,3,4,5whichformsanA.P.\phantom{\rule{0ex}{0ex}}{n}^{th}term\left({T}_{n}\right)=\left(\frac{{n}^{2}+n}{2}\right)\phantom{\rule{0ex}{0ex}}Tofindsumofnterms=\frac{n\left(n+1\right)\left(2n+1\right)}{6}+\frac{n\left(n+1\right)}{2}$

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