Identify the indicated sum for the geometric series. S7 for 162 − 54 + 18 − 6 + .....

Mathematics

1 answer:

Ulleksa [173]2 years ago

3 0

The indicated sum for the geometric series is 121.5

<h3>How to identify the indicated sum for the geometric series?</h3>

The series is given as:

162 − 54 + 18 − 6 + .....

Start by calculating the common ratio of the geometric series.

This is calculated using

r = -54/162

Evaluate

r = -1/3

The indicated sum for the geometric series is then calculated as:

S = a(1 - r^n)/1 - r

Substitute the known values in the above equation

S = 162(1 - (-1/3)^7)/1 + 1/3

Evaluate the exponent and the sum

S = 162(1 + 1/2187)/4/3

Evaluate the sum

S = 162(2188/2187)/4/3

Express as products

S = 162 * (2188/2187)* 3/4

Evaluate the product

S = 162 * 547/729

Evaluate the product

S = 121.5

Hence, the indicated sum for the geometric series is 121.5

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<em><u>Recall:</u></em>

The image attached below shows the relationship between the measure of the central angle and its intercepted arc.

Measure of central angle = its intercepted arc.

Thus, if the measure of a central angle = 57 degrees, based on the angle-arc relationship, the measure of its intercepted arc will also be 57 degrees.

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brainly.com/question/2548029