Question

1. Which of the following can be the nth term of an AP? (4n + 3, 3n2 + 5, n2 + 1) give reason.​

Answer 1

Answer :

4n + 3

Note :

★ A.P. (Arithmetic Progression) : A sequence in which the difference between the consecutive terms are equal is said to be in A.P.

★ A linear polynomial in variable n always represents the nth term of an AP .

★ A quadratic polynomial in variable n always represents the sum of n terms of an AP .

Solution :

• a(n) = 4n + 3 , it can be the nth term of an AP as it is a linear polynomial in variable n .

• a(n) = 3n² + 5 , it cannot be the nth term of an AP as it is not a linear polynomial in variable n .

• a(n) = n² + 1 , it cannot be the nth term of an AP as it is not a linear polynomial in variable n .

Hence ,

(4n + 3) can be the nth term of an AP .