Question

1,2,3,4,........ Sum of first 25 natural integers is
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Answer 1

Answer:

325 Mark as BRAINLIEST!

Step-by-step explanation:

Clearly, it is an Arithmetic Progression whose first term = 1, last term = 25 and number of terms = 25.

Therefore, S = 252

(25 + 1), [Using the formula S = n2

(a + l)]

                = 252

(26)

                = 25 × 13

                = 325

Therefore, the sum of first 25 natural numbers is 325.

Answer 2

Answer:

The sum of first 25 natural numbers = 325

Step-by-step explanation:

Given,

The set of natural numbers 1,2,3,4,.......

To find,

The Sum of first 25 natural numbers

Solution:

Recall the formula,

The sum of first n natural numbers of an AP =

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

Where 'a' is the first term and 'd' is the common difference of the AP

Here,

The set of natural numbers form an AP.

first term = a = 1

Common difference = d =1

n = 25

Then from equation (1) we have

$S_{25} = \frac{25}{2}[2X1 +(25-1)1]$

$S_{25} = \frac{25}{2}[2 +(24]$

$S_{25} = \frac{25X26}{2}$

$S_{25} = 325$

The sum to 25 terms of the AP = 325

∴ The sum of first 25 natural numbers = 325

Alternate method:

The sum of first 'n' natural numbers is given by the formula = $\frac{n(n+1)}{2}$

Substituting the value of n = 25 we get

Sum of first 25 natural numbers = $\frac{25X26}{2}$ = 325

#SPJ2