Question

find the no of terms of the ap 18,15 1/2 ,13...............-49 1/2

Answer 1

Here a=18;d=15 1/2-18=-5/2.

Tn=a+(n-1)d

=>-49 1/2=-99/2=18+(n-1)-5/2

=>5n/2=18+99/2+5/2

=>5n/2=70=>n=28.

Hence it is 28th term.

Hope it helps

Answer 2

Answer:

The no of terms in the given AP is 28.

Step-by-step explanation:

The given arithmetic progression is

$18,15\frac{1}{2},13,...,-49\frac{1}{2}$

First term is 18. So, a=18.

Common difference of AP is

$d=15\frac{1}{2}-18=15+\frac{1}{2}-18=-3+\frac{1}{2}=-2\frac{1}{2}$

The nth term of an AP is defined as

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

Where, a is first term and d is common difference.

$-49\frac{1}{2}=18+(n-1)\times (-2\frac{1}{2})$

$-\frac{99}{2}=18+(n-1)\times (-\frac{5}{2})$

$-\frac{99}{2}-18=(n-1)\times (-\frac{5}{2})$

$\frac{-99-36}{2}=(n-1)\times (-\frac{5}{2})$

Multiply both sides by 2,

$-135=(n-1)(-5)$

Divide both sides by -5.

$27=n-1$

Add 1 on both the sides.

$27+1=n$

$n=28$

Therefore the no of terms in the given AP is 28.