Which term of the A.P : 121, 117, 113, ..., is its first negative term?
[Hint : Find n for a_{n} < 0 ]
Solution:
A sequence that has a common difference between any pair of consecutive numbers is called an Arithmetic Progression.
nth term of an AP is aₙ = a + (n  1)d
Here, a is the first term, d is the common difference and n is the number of terms.
Given:

First Term, a = 121

Common difference, d = 117 121 =  4
We know that n^{th} term of AP,
aₙ = 121+ (n  1) × ( 4)
= 121  4n + 4
= 125  4n
For the first negative term of this A.P,
aₙ < 0
125  4n < 0
125 < 4n
On dividing both sides by 4, we get
n/4 > 125/4
n > 31.25
Therefore, the 32^{nd} term will be the first negative term of this A.P.
☛ Check: NCERT Solutions Class 10 Maths Chapter 5
Video Solution:
Which term of the A.P : 121, 117, 113, ..., is its first negative term?
Class 10 Maths NCERT Solutions Chapter 5 Exercise 5.4 Question 1
Summary:
The first negative term of the A.P : 121, 117, 113, ..., is the 32^{nd }term.
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