How many term are there in the AP 18,151 2 ,13,...,-47? - Vidyadip

Question

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

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Answer

The AP is $18,15\frac{1}{2},13,...,-47$
Here,
$\text{a} = 18$
$\text{d}=15\frac{1}{2}-18=\frac{31}{2}-18=\frac{-5}{2}$
$\text{a}_\text{n}=\text{a}+(\text{n}-1)\text{d}$
$\Rightarrow-47 = 18 + (\text{n}-1 )\Big(\frac{-5}{2}\Big)$
$\Rightarrow-47 = 18 -\frac{5\text{n}}{2}+\frac{5}{2}$
$\Rightarrow\frac{5\text{n}}{2}=47+18+\frac{5}{2}$
$\Rightarrow\frac{5\text{n}}{2}=\frac{94+36+5}{2}$
$\Rightarrow5\text{n}=135$
$\Rightarrow\text{n}=27$
So, the number of terms is 27.

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