Question

25+26+27+28+.........+52=?​

Answer 1

Concept

In an arithmetic progression or an AP, the sum of terms is given by

Sum = n/2 (2a + (n-1)d)

where a =  first term

d = common difference

n = number of terms

Given

25+26+27+28+.........+52

Find

we need to find the sum of the given numbers.

Solution

We have

25+26+27+28+.........+52

Here, we can see that the series is an AP with 1st term 25 and common difference 1

a = 25

d = 1

and the number of terms from 25 to 52 will be 28, so n = 28

Thus, sum will be

Sum = 28/2 ( 2*25 + (28-1) * 1)

= 14 (50 + 27)

= 14 (77)

= 1078

Thus, 25+26+27+28+.........+52 = 1078

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Answer 2

Concept

The formula to calculate the sum of the arithmetic series is given as

Sum = n/2[2a+(n-1)d], where n is the number of the terms, a is the first term and d is the difference of successive terms. Hence we will calculate the sum by using the above formula.

Given

The given series is 25+26+27+28+.........+52.

Find

We have to calculate the sum of the given series by using the above formula.

Solution

Since, n=28

a=25

d=1

Therefore putting these values into the above equation to calculate the sum of the given series.

Sum=28/2[2*25+(28-1)1]

=14[50+27]

=14*77

=1078

Hence the sum of the series 25+26+27+28+.........+52 is equal to 1078.

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