What is the sum of the arithmetic series of odd numbers below?1 + 3 + 5 + ... + 25?

Given from question

a = 1

an = 25

b = a₂ - a = 3 - 1 = 2

Asked from question

Sn

Solution

The general formula for finding the sum of arithmetic series is

Sn = n/2 (a + an)

Because we don't know yet the value of n, we should find it first, with this,

an = a + d (n - 1)

25 = 1 + 2 (n - 1)

25 = 1 + 2n - 2

25 = 2n - 1

2n = 24

n = 12

After finding the value of x, calculate the sum of series by the formula I mentioned above

Sn = n/2 (a + an)

S₁₂ = 12/2 (1 + 25)

S₁₂ = 6 (26)

S₁₂ = 156

The sum of the series is 156