Question

The sequence 15, 21, 27, 33, 39, ...., 75 has 11 terms. Evaluate the related series.

a.) 0420
b.) 495
c.) 0210
d.) 480

Answer 1

b. 495

Explanation:

Given

15, 21, 27, 33, 39, ...., 75

Number of terms = 11

Required

Evaluate

To evaluate means to add up all term of the series above;

The first step is to determine if the series is arithmetic or exponential;

If its arithmetic, then the difference between successive terms must be equal;

In other words;

21 - 15 = 27 - 21 = 33 - 27 = 39 - 33 = 6

Since the result of the above expression gives 6, then it is an arithmetic series;

The sum of n terms of an arithmetic series is calculated as this

`S_n = (n)/(2)(a + T_n)`

Where n = 11

a = First term = 15

T_n = Last term = 75

The formula becomes

`S_(11) = (11)/(2)(15 + 75)`

`S_(11) = (11)/(2)(90)`

`S_(11) = (11 * 90)/(2)`

`S_(11) = (990)/(2)`

`S_(11) = 495`

Hence, the series when evaluated is 495