Question

Prove that the nth term of an ap cannot be n^2+2 justify

Answer 1

In that case, d = a_(n+1) - a_(n) has to be a constant.
Here, a_(n+1) - a_n = 2n + 1, which is not a constant.
Hence, n^2 + 2 cannot be the nth term of an AP.

Answer 2

first write the AP by putting value in the equation

=> n²+2 ,where n=1,2,3

- case 1

=>1²+2=3

- case 2

=>2²+2=6

- case 3

=>3²+2=11

then, the AP will be 3,6,11.....

but in this AP Common Difference is not same

term2 - term1= 3

term3 - term2= 5

that's why this is not an AP

Hence,Proved

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