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Lesson Example Discussion Quiz: Class Homework

Step-3

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	Given an infinite geometric series with the first term (a) equal to 5 and a common ratio (r) equal to \$-1/2\$, find the sum of the series.
2	Step	The given series is an infinite geometric series with the first term	a = 5
3	Step	Common ratio	\$ r = - 1/2 \$
4	Step	The formula for the sum of an infinite geometric series is:	\$ S = a / (1 - r) \$
5	Hint	Substituting a = 5 and \$ r = -1/2\$, we get:	\$ S = 5 / (1 - (-1/2)) \$
6	Step	After simplification	\$ S = 5 / (1 + 1/2) \$ \$ S = 5 / ((2 + 1)/2) = 5 / (3/2) = 10/3 \$
7	Step	Therefore, the sum of the series is \$10/3\$.
8	Choice.A	The sum of the infinite geometric series with a first term of 5 and a common ratio of \$- 1/2\$ is \$10/3\$, not \$13/5\$	\$13/5\$
9	Choice.B	This is the correct answer. It perfectly aligns with the accurate result obtained from the formula	\$10/3\$
10	Choice.C	This value is not the sum of the series with a first term of 5 and a common ratio of \$- 1/2\$	\$-7/2\$
11	Choice.D	This is not the correct answer. It appears to be the result of a different calculation, and it doesn’t match the correct result for this series	\$25/3\$
12	Answer	Option	B
13	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

Given an infinite geometric series with the first term (a) equal to 5 and a common ratio (r) equal to \$-1/2\$, find the sum of the series.

Step

The given series is an infinite geometric series with the first term

a = 5

Step

Common ratio

\$ r = - 1/2 \$

Step

The formula for the sum of an infinite geometric series is:

\$ S = a / (1 - r) \$

Hint

Substituting a = 5 and \$ r = -1/2\$, we get:

\$ S = 5 / (1 - (-1/2)) \$

Step

After simplification

\$ S = 5 / (1 + 1/2) \$

\$ S = 5 / ((2 + 1)/2) = 5 / (3/2) = 10/3 \$

Step

Therefore, the sum of the series is \$10/3\$.

Choice.A

The sum of the infinite geometric series with a first term of 5 and a common ratio of \$- 1/2\$ is \$10/3\$, not \$13/5\$

\$13/5\$

Choice.B

This is the correct answer. It perfectly aligns with the accurate result obtained from the formula

\$10/3\$

Choice.C

This value is not the sum of the series with a first term of 5 and a common ratio of \$- 1/2\$

\$-7/2\$

Choice.D

This is not the correct answer. It appears to be the result of a different calculation, and it doesn’t match the correct result for this series

\$25/3\$

Answer

Option

Sumup

Can you summarize what you’ve understood in the above steps?