Step-2

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 8 − 4 + 2 − 1 + …​ where there are 5 terms in the series

2

Step

The given geometric series is 8,4,2,1,…​

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) = -4/8\$
\$r= -1/2\$

5

Step

From the given data

\$a = 8 ,n = 5\$

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_5 = (8(1-(-1/2)^5))/(1-(-1/2))\$

8

Step

Simplification

\$S_5 = (8(1+(1/2)^5))/(1+(1/2))\$

9

Step

Simplification

\$S_5 = (8(1+(1/32)))/(3/2)\$

10

Step

Simplification

\$S_5 = (8(33/32))/(3/2)\$

11

Step

Simplification

\$S_5 = 8×2×(33/32)/3\$

12

Step

After simplification

\$S_5 = 11/2\$

13

Step

Sum of the 5 terms of geometric series is \$11/2\$

14

Answer

C


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