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 answer is A: S11=(11Ek=11)6+(k-1)2

Answer 2

Answer: The correct option is

(A)
`S_(11)=\sum_(k=1)^(11)6+(k-1)2.`

Step-by-step explanation: We are given to select the correct summation form that represents the sum of the following series :

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

We see that

the first term of the series, a = 6.

And, there is a common difference in any two consecutive terms given by

d = 8 - 6 = 10 - 8 = . . . = 2.

This implies that the given series is arithmetic with first term a = 6 and common difference d = 2.

We know that

the sum of first n terms of an arithmetic series with first term a and common difference d is given by

`a_k=a+(k-1)d.`

Since there are 11 terms in the given series, so the required sum is given by

`S_(11)=\sum_(k=1)^(11)a_k\\\\\Rightarrow S_(11)=\sum_(k=1)^(11)a+(k-1)d\\\\\Rightarrow S_(11)=\sum_(k=1)^(11)6+(k-1)2.`

Thus, (A) is the correct option.