2n - 3 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.
Yes.
According to the question,
aₙ = 2n - 3
Substituting the value of n, we get
n = 1, a₁ = 2(1) - 3 = -1
n = 2, a₂ = 2(2) - 3 = 1
n = 3, a₃ = 2(3) - 3 = 3
n = 4, a₄ = 2(4) - 3 = 5
Hence, the sequence becomes -1, 1, 3, 5….
Calculating the difference, we get,
a₂ - a₁ = 1 - (-1) = 1 + 1 = 2
a₃ - a₂ = 3 - 1 = 2
a₄ - a₃ = 5 - 3 = 2.
So,we get,
a₂ - a₁ = a₃ - a₂ = a₄ - a₃
Therefore, 2n - 3 is the nth term of an AP.
✦ Try This: The first term of an A.P. is 5, the last term is 45 and the sum of all its terms is 400. Find the number of terms and the common difference of the A.P
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5
NCERT Exemplar Class 10 Maths Exercise 5.2 Problem 8 (i)
2n - 3 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. 2n - 3 is the nth term of an AP
☛ Related Questions:
visual curriculum