Step-by-step explanation:
The given series:
[tex]6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24 + 26[/tex]
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
∴ [tex]a_{n}=a+(n-1)d[/tex]
⇒ 6 + (n - 1) 2 = 26
⇒ (n - 1) 2 = 26 - 6 = 20
⇒ n - 1 = [tex]\dfrac{20}{2} =10[/tex]
⇒ n = 10 + 1 = 11
∴ The sum of the given series = [tex]\dfrac{n}{2}(a+a_{n})[/tex]
= [tex]\dfrac{11}{2}(6+26)[/tex]
= [tex]\dfrac{11}{2}(32)[/tex]
= 11 × 16 = 176
Thus, the sum of the given series = 176
