Question

How many terms are there in the AP :
18, 15 and a 1/2, 13............... - 47?

Answer 1

Answer:

Step-by-step explanation:

First term: 18

Common diff : 15.5 -18= -2.5

So,let 'n'th term ne -47

=> a(subscript)n = -47= a+(n-1)d

=>n=27

Answer 2

Answer:

The no of terms in the given AP is 27.

Step-by-step explanation:

The given arithmetic progression is

$18,15\frac{1}{2},13,...,-47$

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.

$-47=18+(n-1)\times (-2\frac{1}{2})$

$-47=18+(n-1)\times (-\frac{5}{2})$

$-47-18=(n-1)\times (-\frac{5}{2})$

$-65=(n-1)\times (-\frac{5}{2})$

Multiply both sides by 2,

$-130=(n-1)(-5)$

Divide both sides by -5.

$26=n-1$

Add 1 on both the sides.

$26+1=n$

$n=27$

Therefore the no of terms in the given AP is 27.