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
[tex]S_n = \frac{n}{2}(a + T_n)[/tex]
Where n = 11
a = First term = 15
T_n = Last term = 75
The formula becomes
[tex]S_{11} = \frac{11}{2}(15 + 75)[/tex]
[tex]S_{11} = \frac{11}{2}(90)[/tex]
[tex]S_{11} = \frac{11 * 90}{2}[/tex]
[tex]S_{11} = \frac{990}{2}[/tex]
[tex]S_{11} = 495[/tex]
Hence, the series when evaluated is 495
