What is the sum of the first 21 terms of the arithmetic series? -5 + (-3) + (-1) + 1 + ... ?

Solution:

If the difference between any two consecutive numbers of a sequence is the same or equal, then it is said to be an arithmetic progression.

To find the sum of 21 terms of this arithmetic progression we use S_n = n / 2 [2a + (n - 1) d]

Given a = - 5

Common difference d = 2

n = 21

Sum of 21 terms  S₂₁ = 21 / 2 [2 (-5) + (21 - 1) 2]

⇒ 21 / 2 [-10 + (20) 2 ]

⇒ 21 / 2 [30]

⇒ 21 × 15

⇒ 315.

Thus, the sum of 21 terms of −5 + (−3) + (−1) + 1 +... is 315.

What is the sum of the first 21 terms of the arithmetic series? -5 + (-3) + (-1) + 1 + ... ?

Summary:

The sum of the first 21 terms of the series -5 + (-3) + (-1) + 1 + ... is 315.