Question

Can 2x^2 + 3 be the nth term of an Arithmetic progression. Justify
your answer.

Answer 1

Given :  2n² + 3   nth term of an AP

To Find : is it possible or not

Solution:

nth term of an AP  =  2n² + 3

(n + 1)th term of AP  = 2(n + 1)²  - 3

common difference = (n + 1)th term of AP - nth term of AP

= 2(n + 1)²  - 3  - (2n² + 3)

= 2(n²  + 2n + 1)  + 3 - 2n² - 3

=  2n² + 4n + 2   - 2n²

=  4n + 2

common difference  is not constant but dependent upon hence it can not be a term of AP

Another ways

1st term = 2(1)² + 3 = 5

2nd term = 2(2)² + 3 = 11

3rd term = 2(3)² + 3 = 21

Difference between 1st two term = 6

and difference between next two terms = 10

Hence common difference is not constant

so 2n² + 3  can not be  nth term of an AP

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