Question

Find the sum of the given series (45+46+47+.........+113+114+115

​

Answer 1

Answer:

Given a series (45+46+47+.

+113+114+115)

We need to find the sum of the given

series

Solution

The given series is in arithmetic progression

So the sum of the series in arithmetic progression is given by

Sum=n/2(a+an) -()

Where

n is number of terms

a is the first term

an is the last term of the series

We need to find the value of n, the number

of terms first

We know that

an=a+(n-1)d -------(ii) From the series an = 115, a= 45

Substituting the value of an = 115 and a=45 in equation (ii) we get,

115=45+(n-1)1

115=45+n-1

115=44+n

n=115-44

n=71

...0.1KB/s * C 70

Substituting the value n=711 in equation (i) we get

Sum=n/2(a+an)

=71/2(45+115)

=71/2x160

=71x80

=5680

Therefore the sum of the series

(45+46+47+.+113+114+115) = 5680

Step-by-step explanation:

$hope \: it \: help \: you$

Answer 2

Answer:

first one

115=45+(n-1)1

115=45+n-1

115=44+n

n=115-44

9=71 =71

second one

=71/2(45+115)

=71/2x160

=71x80

=5680

$\sqrt{hope \: it \: help \: you}$