Which term of the AP: 53, 48, 43,... is the first negative term

Solution:

It is given that

AP: 53, 48, 43,…

First term (a) = 53 and

Common difference (d) = 48 - 53 = -5

Consider the nth term of the AP as the first negative term.

i.e., T_n < 0

We know that the nth term of an AP,

T_n = a + (n - 1)d

Here

⇒ [a + (n - 1 )d] < 0

Substituting the values

⇒ 53 + (n - 1)(-5) < 0

⇒ 53 - 5n + 5 < 0

So we get

⇒ 58 - 5n < 0

⇒ 5n > 58

⇒ n > 11.6

⇒ n = 12

So the 12th term is the first negative term of the given AP

T₁₂ = a + (12 - 1)d

= 53 + 11 (-5)

= 53 - 55

= - 2 < 0

Therefore, the first negative term is the 12th term.

✦ Try This: Which term of the AP: 50, 45, 40,... is the first negative term

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

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NCERT Exemplar Class 10 Maths Exercise 5.3 Problem 17

Which term of the AP: 53, 48, 43,... is the first negative term

Summary:

An arithmetic progression (AP) is a sequence where the differences between every two consecutive terms are the same. In AP: 53, 48, 43,... the first negative term is 12th term.

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☛ Related Questions:

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• 1 + (-2) + (-5) + (-8) + ... + (-236): find the sum