Question

Find the number of terms in ap18,15.5,13 ,,-49.5

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.

HOPE IT HELPS YOU