Question

How many terms are there in the A.P: $18,15\frac{1}{2},13,.......,-47$

Answer 1

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

The first term $a=18$ and

the common difference $d=15\frac{1}{2}-18=-2.5$

the last term is $-47$

Let the last term be the $n^{th}$ term

We know that the $n^{th}$ term of the arithmetic progression is given by $a+(n-1)d$

Therefore, $a+(n-1)d=-47$

$⟹18+(n-1)\ast (-2.5)=-47$

$⟹18+2.5-2.5n=-47$

$⟹20.5-2.5n=-47$

$⟹2.5n=20.5+47$

$⟹n=\frac{67.5}{2.5}$

$⟹n=27$

Therefore, the number of terms in the given sequence is $27$