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

`S_n = (n(a_1 + a_n))/(2)`


`S_6 = (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.

Answer 2

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`