What is the sum of the first 25 odd numbers?

Correct option is C

Given:

We need the sum of the first 25 odd numbers.

Concept Used:
The sum of the first n odd numbers is $$n^2$$​​

Solution:

Sum =$$25^2 = 625$$

Alternate Method:

The first 25 odd numbers form an arithmetic progression: 1, 3, 5, ..., 49.

First term (a) = 1

Common difference (d) = 2

Number of terms (n) = 25

Last term (l) = a + (n - 1)d

l = 1 + (25 - 1) $$\times$$2

l = 1 + 24$$\times$$2

l = 1 + 48 = 49

Sum$$(S_n)$$​ = $$\frac n2$$​ (a + l)

​$$S_n$$​=$$\frac{25}2$$​ (1 + 49)

​$$S_n$$​= $$\frac{25}2$$​ $$\times$$50

​$$S_n$$​= 25$$\times$$25 = 625

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

​