Question

Find the number of terms of ap 18, 15.5, 13......., -49.5 and find the sum of all terms

Answer 1

Answer:

The sum of all terms is -441.

Step-by-step explanation:

The given AP is

18, 15.5, 13......., -49.5

Here first term is 18 and the common difference is -2.5.

$15.5-18=-2.5$

The nth term of an AP is

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

$-49.5=18+(n-1)(-2.5)$

$-49.5-18=(n-1)(-2.5)$

$-67.5=(n-1)(-2.5)$

$27=(n-1)$

$n=28$

The number of term is 28.

The sum of n terms of an AP is

$S_n=\frac{n}{2}[2a+(n-1)d]$

The sum of 28 terms is

$S_{28}=\frac{28}{2}[2(18)+(28-1)(-2.5)]$

$S_{28}=14[36-67.5]$

$S_{28}=-441$

Therefore the sum of all terms is -441.