Sum of first P terms of an ap is a p square + b p find its common diff

1.	Sum of first P terms of an ap is a p square + b p find its common difference
Answer» We are given that sum\xa0of first p terms of this APSp= ap2 + bpLet the first term= x and common difference = d{tex}{\\mathrm S}_1=\\mathrm a(1)^2+\\mathrm b(1)=\\mathrm a+\\mathrm b{/tex}So first term x = a+bNow S2 = a(2)2 + b(2)S2 = 4a + 2b,{tex}\\mathrm{So}\\;{\\mathrm s}_2={\\mathrm a}_1+{\\mathrm a}_2=\\mathrm x+\\mathrm x+\\mathrm d=4\\mathrm a+2\\mathrm b{/tex}2x + d = 4a+2b2(a+b)+d = 4a+2b2a+2b+d=4a+2bd=4a+2b-2a-2bd = 2aTherefore, the common difference of the given AP is 2a.

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