Question

Which term fo the AP 121, 117, 113, .. is its first negative term?

Answer 1

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

First term, a = 121

Common difference, d = 117-121 = -4

Let nth term be the first negative term of the AP.

Now, nth tern = a + (n-1) $\times$ d

= 121 + (n - 1) $\times$ (-4)

= 121 - 4n + 4

= 125 - 4n

Now, we have to find the suitable value of n so that the value of (125 - 4n) is negative.

So, 125 - 4n < 0

=> 125 < 4n

=> 4n > 125

=> n > 125/4

=> n > 31.25

Since the term can not be in decimal form (term is always taken a positive integer)

So, n = 32