Lesson Example Discussion Quiz: Class Homework |
Step-2 |
Title: Infinite sequence and series |
Grade: 10-a Lesson: S2-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 infinite arithmetic series \$3 + 7 + 11 + 15 + ...\$. |
|
2 |
Step |
The given series is an arithmetic series with the first term |
a = 3 |
3 |
Step |
Common difference |
d = 4 |
4 |
Formula: |
The formula for the sum of an arithmetic series is: |
\$ S = n/2 * (2a + (n-1)d) \$ |
5 |
Step |
Substituting a = 3, d = 4 and \$ n = \infty \$, we get: |
\$ S = \infty \$ |
6 |
Step |
Therefore, the sum of the given series is infinity. |
|
7 |
Choice.A |
The series diverges, meaning it does not converge to a finite value and continues infinitely |
Infinity |
8 |
Choice.B |
The series doesn’t converge to 0; it increases indefinitely with a common difference of 4 |
0 |
9 |
Choice.C |
This is incorrect. The series doesn’t converge; it diverges to infinity |
Converges |
10 |
Choice.D |
This choice is incorrect. The series diverges to infinity; it doesn’t have a finite sum |
Diverges |
11 |
Answer |
Option |
A |
12 |
Sumup |
Can you summarize what you’ve understood in the above steps? |
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