Question

Which term is the first negative term in the given A.P:23,21.5 ,20....?

Answer 1

Here,a=23
d=-1.5 (for complete solution please see the attached screenshot

Answer 2

Answer:

The 17th term is the first negative term in the given A.P, i.e. -1.

Step-by-step explanation:

The given AP is

23,21.5 ,20....

The first term is 23 and the common difference is -1.5.

$a=23, d=-1.5$

The nth term of an AP is

$a_n=a+(n-1)d$

$a_n=23+(n-1)(-1.5)$

nth term is negative.

$a_n<0$

$23+(n-1)(-1.5)<0$

$23-1.5n+1.5<0$

$24.5-1.5n<0$

$24.5<1.5n$

$\frac{24.5}{1.5}<n$

$16.333<n$

It means for negative terms the value of n must be greater than 16.33. The first negative term is 17 th term.

$a_{17}=23+(17-1)(-1.5)$

$a_{17}=23+(16)(-1.5)=-1$

Therefore the 17th term is the first negative term in the given A.P, i.e. -1.