Question

find the number of terms in each of the following APs:

18,15 1/2,,13,.....,-47

Answer 1

so there are 27 terms in total

Answer 2

Answer: There are 27 terms in the sequence.

Step-by-step explanation:

Since we have given that

$18,15\frac{1}{2},13,......-47\\\\18,\frac{31}{2},13,.........-47$

Here, first term = a = 15

d = common difference is given by

$a_2-a_1\\\\=\frac{31}{2}-18\\\\=\frac{31-36}{2}=\frac{-5}{2}=-2.5$

And the last term is given by

$a_n=-47$

We need to find the number of terms 'n':

$a_n=a+(n-1)d\\\\-47=18+(n-1)(-2.5)\\\\-47-18=(n-1)(-2.5)\\\\-65=(n-1)(-2.5)\\\\\frac{65}{2.5}=n-1\\\\26=n-1\\\\n=27$

Hence, there are 27 terms in the sequence.