the arithmetic mean of the series a+a+d+a+2d......(a+2nd) {ans is a+nd) Share with your friends Share 0 Sandeep Saurav answered this Dear Student, The given Series is a, a+d, a+2d, a+3d, ..., a+2ndSo, its first term=aand common difference=dand mth term=a+2ndlet no. of terms be mSo, am=a+(m-1)d⇒a+2nd=a+(m-1)d⇒2nd=(m-1)d⇒2n=(m-1)⇒m=2n+1So, nowSm=m2(a+am)⇒Sm=2n+12(a+a+2nd)⇒Sm=2n+12(2a+2nd)⇒Sm=2n+122(a+nd)⇒Sm=(2n+1)(a+nd)So, Arithmetic Mean=Smm=(2n+1)(a+nd)(2n+1)=a+ndHence Arithmetic Mean of the Series is a+nd. Regards 0 View Full Answer
