The nth term of an AP cannot be n² + 1. Justify your answer
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.
Given in the question,
aₙ = n² + 1.
Substituting the values, we get,
a₁ = 1² + 1 = 2
a₂ = 2² + 1 = 5
a₃ = 3² + 1 = 10
The sequence becomes 2, 5, 10, ...
a₂ - a₁ ≠ a₃ - a₂
5 - 2 ≠ 10-5,
Therefore, the above statement does form an A.P.
✦ Try This: Find the 9th term from the end (towards the first term) of the A.P. 5,9,13, …, 185
The nth term of an AP is
aₙ = a + (n - 1 )d.
a = first term
aₙ = nth term
d = common difference
As per the question,
5 + (n - 1) 4 = 185
5 + 4n - 4 = 185
4n + 1 = 185
4n = 184
n = 46
Here the 9th term from the end will be the 38th term of AP
a + 37d = 5 + 37 (4) = 153
Therefore, the 9th term from the end is 153.
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5
NCERT Exemplar Class 10 Maths Exercise 5.2 Sample Problem 3
The nth term of an AP cannot be n² + 1. Justify your answer
Summary:
An arithmetic progression (AP) is a sequence where the two consecutive terms have the same common difference. The nth term of an AP cannot be n² + 1
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