Question

The given series has six terms. What is the sum of the terms of the series?

5 + 8 + 11 + . . . + 20

44

64

75

55

Answer 1

Given that there are six terms, we have this set:

$a_{n} = \{5,8,11,a_{4},a_{5},20}\}$

So, we need to find a4 and a5. Given that:

8-5 = 3
11-8 = 3

Then, it is obvious that

$a_{4}-11 = 3$ ∴ $a_{4}=14$ 
$a_{5}-14 = 3$ ∴ $a_{5}=17$ 

Then, the sum of the terms of the series is:

$S = 5+8+11+14+17+20 = 75$

Answer 2

$S_n = \dfrac{n(a_1 + a_n)}{2}$

$S_6 = \dfrac{6(5 + 20)}{2}$

$S_6 = 75$

Of course, you can just add the 6 terms, 5, 8, 11, 14, 17, and 20, and you will also get a sum of 75.