Question

How many terms are there in the $AP=18,15\frac{1}{2},13,...,-47?$

Answer 1

The given AP is $AP=18,15\frac{1}{2},13,...,-47$

First term, $a=18$

Common difference, $d=\frac{31}{2}–18=\frac{-5}{2}$

Suppose there are$n$ terms in the given AP.

Then, $a_n$ = −47

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

⇒$18+(n–1)\times \left(\frac{-5}{2}\right)=–47$
⇒$\left(\frac{-5}{2}\right)(n–1)=–65$
⇒$n–1=-65\times \left(\frac{-2}{5}\right)=26$

⇒$n–1=26$
⇒$n=27$

Hence, there are $27$ items in the given AP.