Which term of the sequence 17, 161/5, 152/5, 143/5, ........... is the first negative term?

The first term is :

The second term is : 

The third term is : 

The fourth term is : 

Hence the given series is an arithmetic progression.

We need to find the first negative term in the series.

Here,

nth term is:

Let nth term be negative.

We need to find such that:

Since n is a natural number, we need to take the lowest possible value of n such that n is greater than .

th term in the series would be negative.

Hence it is verified that 23rd term in the series turns negative.

  • 12

Let the nth term be the first -ve term. Here a = 17 , d = -4/5.

N th term of an A.P. = a+(n-1)*d = 17 + (n-1) * -4/5 = 17 -4n/5 + 4/5 = (89 - 4n)/5.

We need to find the value of n which would give us a -ve number.

If we put n = 23 we get the value of the nth term as (89-4*23)/5 = (89-92)/5 = -3/5

So the 23rd term would be the first -ve term.

Cheers.!!!!!!!!!!!!!!!!

  • -6
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