1+n+n² is the nth term of an AP?

Solution:

An arithmetic progression (AP) is a sequence where the two consecutive terms have the same common difference. It is obtained by adding the same fixed number to its previous term.

No.

According to the question,

aₙ = 1 + n + n²

Substituting the values of n, we get,

n = 1, a₁ = 1 + 1 + (1)² = 3

n = 2, a₂ = 1 + 2 + (2)² = 1 + 2 + 4 = 7

n = 3, a₃ = 1 + 3 + (3)² = 1+ 3 + 9 = 13

Hence, the sequence becomes 3, 7, 13,…

Calculating the difference, we get,

a₂ - a₁ = 7 - 3 = 4

a₃ - a₂ = 13 - 7 = 6.

So, we get,

a₂ - a₁ ≠ a₃ - a₂

Since, the difference of each successive term is not the same, it does not form an AP.

Therefore,it does not form an AP.

✦ Try This: The sum of first n terms of an AP is 3n2 + 4n. Find the 25th term of this AP

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5

NCERT Exemplar Class 10 Maths Exercise 5.2 Problem 8 (iii)

1+n+n² is the nth term of an AP?

Summary:

An arithmetic progression is a sequence where each term, except the first term, is obtained by adding a fixed number to its previous term. 1+n+n² does not form an AP

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