Question

Which term of the AP: 121, 117, 113, . . ., is its first negative term?
Please answer quick

Answer 1

The general term or nth term of A.P is given by an = a + (n – 1)d,
where a is the first term, d is the common difference and n is the number of term.
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Solution:

Given:first term(a)= 121 
common difference (d)= 117- 121 = -4
∵ n th term of an AP

an = a + (n – 1)d
⇒121+(n-1) ×(-4)
⇒121-4n+4
⇒12+4-4n
⇒125 -4n
an= 125 -4n

For first negative term , an <0
⇒ 125-4n<0
⇒125<4n
⇒4n>125
⇒n>125/4
⇒n> 31 1/4

least integral value of n= 32

Hence, 32nd term of the given AP is the first negative term. 

Answer 2

Let a be the first term and d be a common difference.

Given AP is 121,117,113....

First-term a = 121.

Common difference d = 117 - 121

                                      = -4.


Let nth term is the first negative term in the AP.

= > an = a + (n - 1) * d

           = 121 + (n - 1) * d

           = 121 + (n - 1) * (-4)

           = 121 + 4n - (-4)

           = 125 + 4n

 

For the first negative term, an < 0.

= > 125 - 4n < 0

= > 125 < 4n

= > 4n > 125

= > n > 125/4

= > n > 31.25


Therefore the first negative term is the 32nd term.


Hope this helps!