In an AP, if Sₙ = n(4n + 1), find the AP
Solution:
Given, the expression for the sum of the terms is Sₙ = n(4n + 1)
We have to find the AP.
Put n = 1,
S₁ = 1(4(1) + 1) = 4 + 1 = 5
Put n =2,
S₂ = 2(4(2) + 1) = 2(8 + 1) = 2(9) = 18
The AP in terms of common difference is given by
a, a+d, a+2d, a+3d,......., a+(n-1)d
So, S₁ = a
First term, a = 5
S₂ = sum of first two terms of an AP
= a+ a + d
= 2a + d
To find the common difference d,
2a + d = 18
2(5) + d = 18
10 + d = 18
d = 18 - 10
d = 8
The series can be framed as
a = 5
a + d = 5 + 8 = 13
a + 2d = 5 + 2(8) = 5 + 16 = 21
a + 3d = 5 + 3(8) = 5 + 24 = 29
Therefore, the series is 5, 13, 21, 29,.....
✦ Try This: In an AP, if Sₙ = n(2n - 1), find the AP
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5
NCERT Exemplar Class 10 Maths Exercise 5.3 Problem 24
In an AP, if Sₙ = n(4n + 1), find the AP
Summary:
An arithmetic progression (AP) is a sequence where the differences between every two consecutive terms are the same. In an AP, if Sₙ = n(4n + 1), the AP is 5, 13, 21, 29,......
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