Question

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

Answer 1

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

$\huge\bold{Solution-;}$

Let there be n terms in the given A.P ..Then,

$a_{n} \: (nth \: term) = a + (n - 1)d = - 47$

Here ,
$a = 18 \: \: and \: \: d \: = - 2 \frac{1}{2}$
$1 8 + (n - 1)( - 2 \frac{1}{2} ) = - 47 \\ \rightarrow - 2 \frac{1}{2} (n - 1) = 65 \\ \\ \rightarrow \: n - 1 = 26 \\\rightarrow \: n = 27$

$\big] \Big] \bigg] \Bigg]Hence ,\: there\: are\ 27\: terms\: in\: the\: A.P.\big] \Big] \bigg] \Bigg]$