Question

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

Answer 1

Answer:

b. 495

Step-by-step 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

$S_n = \frac{n}{2}(a + T_n)$

Where n = 11

a = First term = 15

T_n = Last term = 75

The formula becomes

$S_{11} = \frac{11}{2}(15 + 75)$

$S_{11} = \frac{11}{2}(90)$

$S_{11} = \frac{11 * 90}{2}$

$S_{11} = \frac{990}{2}$

$S_{11} = 495$

Hence, the series when evaluated is 495