Question

Find the no of the terms in the AP:18,31/2,13,...............-47

Answer 1

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Answer 2

Answer:

The number of the terms in the given AP is 27.

Step-by-step explanation:

The given AP is

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

Here the first term is 18 and the common difference is

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

The nth term of an AP is

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

$-47=18+(n-1)(-2.5)$

$-47=18-2.5n+2.5$

$-47=21.5-2.5n$

$-47-20.5=-2.5n$

$-67.5=-2.5n$

Divide both sides by -2.5.

$27=n$

Therefore the number of the terms in the given AP is 27.