Step-3

Title: Geometric progression

Grade: 9-a Lesson: S4-L7

Explanation: Hello Students, time to practice and review the steps for the problem.

Lesson Steps

Step Type Explanation Answer

1

Problem

Find the sum of the geometric series –7 – 21 – 63 – …​ where there are 12 terms in the series

2

Step

The given geometric series is 7,21,63…​

3

Step

We know that geometric progression is a series of numbers in which each term is obtained by multiplying the previous term by a fixed number, known as the common ratio.

4

Formula:

common ratio of the given geometric series is given by

\$ r = (r_2)/(r_1) = -21/-7 = 3\$

5

Step

From the given data

\$a = -7 ,n =12\$

6

Formula:

Sum of the first n terms \$S_n = (a(1-r^n))/(1-r)\$

7

Step

Substitute the values in the formula

\$S_12 = (-7(1-3^12))/(1-3)\$

8

Step

Simplification

\$S_12 = (-7(1-531441))/-2\$

9

Step

Simplification

\$S_12 = 3720080/-2\$

10

Step

After simplification

\$S_12 = -1860040\$

11

Step

Sum of the 12 terms of geometric series is -1860040

12

Answer

D


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