Lesson Example Discussion Quiz: Class Homework |
Step-5 |
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 40,-20,10,-5,5/2,-5/4 |
|
2 |
Step |
The given geometric series is 40,-20,10,-5,5/2,-5/4 |
|
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) = -20/40 = -1/2\$ |
5 |
Step |
From the given data |
\$a = 40 ,n =6\$ |
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_6 = (40(1-(-1/2)^6))/(1-(-1/2))\$ |
8 |
Step |
Simplification |
\$S_6 = (40(1+(1/2)^6))/(1+(1/2))\$ |
9 |
Step |
Simplification |
\$S_6 = (40(1+(1/32)))/(3/2)\$ |
10 |
Step |
Simplification |
\$S_6 = (40(33/32))/(3/2)\$ |
11 |
Step |
Simplification |
\$S_6 = (315/8)/(3/2)\$ |
12 |
Step |
Simplification |
\$S_6 = (315×2)/(8×3)\$ |
13 |
Step |
Simplification |
\$S_6 = 315/12\$ |
14 |
Step |
After simplification |
\$S_6 = 105/4\$ |
15 |
Step |
Sum of the 6 terms of geometric series is 728 |
|
16 |
Answer |
A |
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