Question

Find sum of an given AP 72+70+68.......+40

Answer 1

Given,

An A.P 72,70...40

To Find,

The sum of the A.P

Solution,

In the given A.P

a = 72

d = 70-72 = -2

Now,

aₙ = a+(n-1)d

40 = 72+(n-1)(-2)

-32 = -2n+2

-34 = -2n

n = 17

Sum of the A.P = n/2(a+aₙ)

                          = 17/2(72+40)

                          = (17)(56)

                          = 952

Hence, the sum of the A.P is 952.

Answer 2

Concept

Arithmetic progression or arithmetic sequence is a number sequence in which the difference between consecutive terms is constant.

Given

Series is $72+70+68+.....+40$

Find

We are asked to find the sum of the given series

Solution

$72+70+68+.....+40\\a_{n}=a+(n-1)d\\40=72+(n-1)(-2)\\-32=-2n+2\\-34=-2n\\n=17$

$S_{n} =\frac{n}{2}(a+l)\\ S_{n} =\frac{17}{2}(72+40)\\ S_{n} =\frac{17}{2} (112)\\ S_{n} =17 \times 56\\ S_{n} =952$

Hence the sum of the given series is 952.