Question

the nth term of an AP cannot be 3n^2+5. Justify your answer

Answer 1

Let's say it is the nth term of AP .

nth term = 3n² + 5

So,

1st term (n = 1) = 3(1)² + 5 = 8

2nd term (n = 2) = 3(2)² + 5 = 17

3rd term (n = 3) = 3(3)² + 5 = 32

If it's nth term of AP then their common difference must be same.

Common difference (d) is

2nd term - 1st term = 17 - 8 = 9

3rd term - 2nd term = 32 - 17 = 15

So, common difference is not same

( 9 ≠ 15 )

Hence, It's not the nth term of an AP.

PROVED.....

Answer 2

plz refer to this attachment