Question

find the sum of the first 25 odd natural number​

Answer 1

Answer:

625

The number series 1, 3, 5, 7, 9, . . . . , 49. Therefore, 625 is the sum of first 25 odd numbers.

Step-by-step explanation:

step 1 Address the formula, input parameters & values.

Input parameters & values:

The number series 1, 3, 5, 7, 9, .  .  .  .  , 49.

The first term a = 1

The common difference d = 2

Total number of terms n = 25

step 2 apply the input parameter values in the AP formula

Sum = n/2 x (a + Tn)

= 25/2 x (1 + 49)

= (25 x 50)/ 2

= 1250/2

1 + 3 + 5 + 7 + 9 + .  .  .  .   + 49 = 625

Therefore, 625 is the sum of first 25 odd numbers.

Answer 2

Answer:

Required sum is 625.

Step-by-step explanation:

First 25 odd natural numbers are

$1,3,5,7,9,11,13,15.........,45,47,49...$

Now we want to find sum of these numbers.

Basically this is a AP series.

We know Sum of terms in AP series

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

Where a is the 1st term,

n is number of term and d is difference of two term.

So Sum$= \frac{25}{2} (2 \times 1 + (25 - 1)2) = \frac{25}{2} (2 + 48) = \frac{25}{2} \times 50 = 25 \times 25 = 625$

Required sum is 625.