An important question from ML Agarwal of Class10 for board examination We have been asked Justify whether it is true to say that the following are the nth term of an AP? (ii) n²+1

ML Agarwal (avichal publication), Class 10, Arithmetic Progression chapter 9, question no. 27(ii)

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# Justify whether it is true to say that the following are the nth term of an AP? (ii) n²+1

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## an=1+n+n2

a1=1+1+12=3

a2=1+2+22=7

a3=1+3+32=13

a4=1+4+42=21

a5=1+5+52=31

So, d1=a2−a1=7−3=4

d2=a3−a2=13−7=6

d3=a4−a3=21−13=8

d4=a5−a4=31−21=10

As d1=d2, so, an=1+n+n2 is not the nth term of an A.P.