3n² + 5 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 = 3n² + 5

Substituting the value of n, we get,

n = 1, a₁ = 3(1)2 + 5 = 8

n = 2, a₂ = 3(2)2 + 5 = 3(4) + 5 = 17

n = 3, a₁ = 3(3)2 + 5 = 3(9) + 5 = 27 + 5 = 32

Hence, the sequence becomes 8, 17, 32,….

Calculating the difference, we get,

a₂ - a₁ = 17 - 8 = 9

a₃ - a₂ = 32 -17 = 15.

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 nth term of an A.P. is given by (-4n + 15). Find the sum of the first 20 terms of this A.P

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

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

3n² + 5 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. 3n² +5 does not form an AP

☛ Related Questions:

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