Question

which term of AP ,121, 117 ,113 is its first negative term

Answer 1

Hi,

Here is your answer,

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

Credit goes to = Nikitasingh.

Answer 2

Hey there !

Given AP = 121, 117, 113, ....

So First term ( a ) = 121

Common Difference ( d ) = ( - 4 )

Let the term to be found be aₓ

Also we have to find the first negative term. So we can say that aₓ < 0

=> aₓ = a + ( x - 1 ) d

Here x represents the number of terms.

So aₓ = 121 + ( x - 1 ) -4

=> aₓ = 121 - 4x + 4

=> aₓ = 125 - 4x

We also know that aₓ < 0

=> 125 - 4x < 0

=> 125 < 4x

=> 125 / 4 < x

=> 31.25 < x

Therefore the nearest term 32 can be taken to be less tan zero.

Hence 32nd term is the first negative term to be attained in the given AP.

Hope my answer helped !