Factorial Notation

Infinite Sequence

Finite Sequence

General Term of a Sequence

Arithmetic Sequence

Geometric Sequence

Annuity

Partial Sum

Summation Notation

Factorial Notation

As an inventory analyst, you record the total number of items restocked at the end of each week. You list the totals so that the first week corresponds to position 1, the second week to position 2, and so on. In algebraic terms, this ordered list of values—which can be thought of as a mathematical relationship whose domain is restricted to the counting numbers (${}1, 2, 3, \dots$)—is formally defined as a:

In a workplace productivity report, a supervisor lists the number of units produced in each consecutive hour of a shift. Algebraically, this ordered list represents a sequence. True or False: An algebraic sequence is formally defined as a function whose domain is restricted to the set of counting numbers (${}1, 2, 3, \dots$).

A customer service lead tracks the number of calls answered during each hour of an 8-hour shift. Match each algebraic component of this data record with its practical description.

Identifying Components of Sequential Data

A supervisor at a manufacturing plant maintains a production log that lists the number of units completed during each consecutive hour of a shift. This ordered list of data (e.g., ${}45, 52, 48, \dots$) represents an algebraic sequence. In this context, each individual numerical value in the list is formally referred to as a(n) ____.

Defining Sequential Logistics Logs

In your role as a logistics coordinator, you are tracking the total number of shipments processed during each consecutive hour of a morning shift. You record the following data:

• Hour 3 (Position 3): 42 shipments
• Hour 1 (Position 1): 35 shipments
• Hour 4 (Position 4): 50 shipments
• Hour 2 (Position 2): 38 shipments

Because an algebraic sequence is an ordered list of terms whose domain is restricted to the counting numbers (${}1, 2, 3, 4$), arrange these shipment counts in the correct order to represent the sequence starting from the first term (corresponding to domain value ${}1$) to the fourth term (corresponding to domain value ${}4$).