if the sum of first (n+1) terms of an arithmetic sequence is pn2+qn+r ; then show that p+r=q - Maths - Arithemetic Sequences

Question

if the sum of first (n+1) terms of an arithmetic sequence is
pn2+qn+r ; then show that p+r=q

Sandeep Saurav · Accepted Answer

Dear Student,

Sum of first n terms of an AP is given by sn=n2{2a+(n-1)d}so, sn+1=n+12{2a+(n+1-1)d}sn+1=n+12{2a+nd}sn+1=2an+n2d+2a+nd2sn+1=dn22+(2a+d)n2+2a2sn+1=dn22+(2a+d)n2+a
1and it is given that sn+1=pn2+qn+r
2comparing 1 and 2p=d2, q=2a+d2 and r=aNow adding p+r⇒p+r=d2+a=d+2a2⇒p+r=d+2a2⇒p+r=q

Regards

if the sum of first (n+1) terms of an arithmetic sequence is pn2+qn+r ; then show that p+r=q.

if the sum of first (n+1) terms of an arithmetic sequence is pn²+qn+r ; then show that p+r=q.