Learn Before
Example: Finding the Fifteenth Term of an Arithmetic Sequence
Find the fifteenth term of an arithmetic sequence where the first term is and the common difference is .
Use the general term formula with , , and :
Substitute the values:
Simplify inside the parentheses:
Multiply and then add:
The fifteenth term of the sequence is 87.
0
1
Tags
OpenStax
Intermediate Algebra @ OpenStax
Ch.12 Sequences, Series and Binomial Theorem - Intermediate Algebra @ OpenStax
Algebra
Related
Example: Finding the Fifteenth Term of an Arithmetic Sequence
Example: Finding a Term Given Another Term and the Common Difference
Example: Finding the First Term and Common Difference Given Two Terms
In a technician certification program, a trainee's daily repair target follows an arithmetic sequence. Match each component of the general term formula, , with its correct meaning in this professional training context.
A production supervisor uses an arithmetic sequence to plan a gradual increase in daily output at a manufacturing plant. To find the specific output target for any given day (), the supervisor must apply the general term formula. If represents the output on the first day and represents the constant daily increase, which formula correctly calculates the target for day ?
A corporate trainer is scheduling a series of webinars where the number of participants increases by a constant amount each session, forming an arithmetic sequence. To calculate the number of participants for any session , the trainer uses the general term formula . Is it true or false that the component in this formula represents the total number of times the daily increase is added to the first session's count ?
Formula for Projecting Daily Production
A quality control inspector tracks a machine's output, which increases following an arithmetic sequence. Based on the logical pattern used to derive the general term formula, , arrange the following expressions for the first four terms of the sequence in their correct order, starting with the first term.
Learn After
A production supervisor is tracking the daily output of a newly calibrated machine. On the first day, the machine produces 3 parts. The supervisor plans to increase the machine's output by exactly 6 parts each day. To report the projected output for the 15th day, the supervisor needs to recall the general term formula for an arithmetic sequence. Which of the following setups correctly substitutes the given values into the formula to find the 15th term?
A corporate training coordinator is scheduling a series of workshops. For the first session, they enroll 3 participants. They plan to increase the enrollment by 6 participants for each subsequent session. Following the arithmetic sequence example where the first term is 3 and the common difference is 6, the total number of participants enrolled for the 15th session will be ____.
A customer success manager is analyzing the growth of a new subscription service. The service began with 3 active subscriptions in its first month and has consistently added 6 new subscriptions each month. Based on the worked example that calculated the total for the 15th month, match each variable from the arithmetic sequence formula to its corresponding value or role in this scenario.
A project manager is tracking the growth of a client's social media following. The account started with 3 followers and grows by 6 followers every day. Following the method used in the arithmetic sequence example, arrange the following steps in the correct order to find the number of followers on the 15th day.
A facilities manager is tracking the installation of security cameras on Day 1, with an increase of cameras every day thereafter. True or False: According to the general term formula as applied in the example to find the 15th day's total, the common difference of must be multiplied by before adding the first term.