Question

Which term of the A.P 120,116,112,.....is its first negative term

Answer 1

32nd term is the first negative term of A.P 120,116,112,...

Given:

• An A.P.
• 120,116,112,...

To find:

• Which term is first negative term of given AP.

Solution:

Formula/Concept to be used:

General term of A.P.:$\bf a_n = a + (n - 1)d$

here,

a: first term

d: Common difference

an: nth term

n: number of terms

Step 1:

Write the values from AP.

a= 120

d=116-120

or

d= -4

Let an is 0,because AP is descending,so all terms less than 0 are negative terms.

Step 2:

Solve the in-equation for less than zero.

$120 + (n - 1)( - 4) < 0$

or

$- 4(n - 1) < - 120$

or

$4(n - 1) > 120$

[Multiplication of -1 changes the sign of inequality]

or

$n - 1 > \frac{120}{4}$

or

$n - 1 > 30$

or

$\bf n > 31$

Thus,

Up to 31 terms, all the terms of given A.P. are positive.

*Number of terms are integers.

So,

As soon as the value of n is greater than 31, the terms of AP will be negative.

Step 3:

Justification.

Find the 32nd term of A.P.

$a_{32}=120 + (32 - 1)( - 4)$

or

$a_{32}=120 -124$

or

$\bf a_{32}=-4$

Thus,

32nd term is the first negative term of A.P.120,116,112,...

Learn more:

1) Which term of AP 129, 125, 121, .... is its first negative term? Give full solutions.

:)

https://brainly.in/question/2732485

2) Which term of AP, 100, 97, 94, 91,... will be its first -ve term ?

https://brainly.in/question/5031643