Question

Which of the following represents the sum of the series? 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24 + 26

Answer 1

The sum of the given series = 176

Step-by-step explanation:

The given series:

$6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24 + 26$

Here, first term(a) = 6 and common difference(d) = 8 - 6 = 2

The given series are in AP.

Let the number of term = n

We know that,

The nth term of an AP

∴ $a_{n}=a+(n-1)d$

⇒ 6 + (n - 1) 2 = 26

⇒ (n - 1) 2 = 26 - 6 = 20

⇒ n - 1 = $\dfrac{20}{2} =10$

⇒ n = 10 + 1 = 11

∴  The sum of the given series = $\dfrac{n}{2}(a+a_{n})$

= $\dfrac{11}{2}(6+26)$

= $\dfrac{11}{2}(32)$

= 11 × 16 = 176

Thus, the sum of the given series = 176