Lesson Example Discussion Quiz: Class Homework |
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 |
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2 |
Step |
The given geometric series is 8,4,2,1,… |
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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. |
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4 |
Formula: |
common ratio of the given geometric series is given by |
\$ r = (r_2)/(r_1) = -4/8\$ |
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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