Lesson Example Discussion Quiz: Class Homework |
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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