General Mathematics Unit 3: Arithmetic Sequences

This set of flashcards covers vocabulary and key concepts related to arithmetic sequences, including formulas, representations, and worked examples from the lecture transcript.

Arithmetic Sequence

A sequence of numbers in which each term after the first is obtained by adding a constant value to the preceding term.

Common Difference

The constant value, denoted as $d$, added to each term in an arithmetic sequence to determine the next term.

Arithmetic Progression

Another name used to refer to an arithmetic sequence.

Increasing Sequence Condition

The condition where the common difference is greater than zero, or $d > 0$.

Decreasing Sequence Condition

The condition where the common difference is less than zero, or $d < 0$.

Numerical Representation

A form that presents terms in a numbered list to highlight consistent patterns of change between consecutive terms.

Visual Representation

The use of graphical tools such as dot arrays or block arrangements to depict the uniform increase and structure of a sequence.

General Form Formula

$$a_n = a_1 + (n - 1)d$$

$$a_1$$

The symbol representing the first term of the arithmetic sequence in the general formula.

$$n$$

The symbol representing the term number in the general formula for an arithmetic sequence.

$$d$$

The symbol representing the common difference in an arithmetic sequence formula.

$$a_n$$

The symbol used to denote the nth term of an arithmetic sequence.

Common difference of 2, 5, 8, 11, 14, 17

$$3$$

10th term of the sequence 2, 5, 8, 11, 14, 17

$$29$$

Common difference calculation for $a_1 = 5$ and $a_{10} = 50$

$$5$$

Number of terms ($n$) for $a_1 = 4$, $a_n = 40$, and $d = 6$

$$7$$

First term ($a_1$) for $a_{12} = 77$ and $d = 6$

$$11$$

First six terms of a sequence where $a_1 = 3$ and $d = 4$

$$3, 7, 11, 15, 19, 23$$

Common difference for the sequence 5, 11, 17, 23, 29

$$6$$

12th term for the sequence 5, 11, 17, 23, 29

$$71$$

Student save amount in first week (given $a_{10} = ₱280$ and $d = ₱20$)

$$₱100$$

Student save amount in 20th week (given $a_{10} = 280$ and $d = 20$)

$$₱480$$

Businessman's daily additional deposit

$$₱500$$

Businessman's total deposit by the 15th day

$$₱12,000$$

Consecutive Terms

Terms that follow directly after one another in a sequence.

Preceding Term

The specific term that comes directly before the current term being identified.

Algebraic Manipulation

The process of rearranging the general formula to solve for other unknown quantities like $d$, $n$, or $a_1$.

Graphical Tools

Models like dot arrays or block arrangements that provide a concrete illustration of uniform increases.

Unit 3 Title

Sequences and Series

Predictable Pattern

A sequence of events or numbers that follows a consistent rule, such as fitness routines or financial savings.

Common Difference logic

A value found by subtracting any term by the term immediately before it.

Arithmetic sequence dot pattern 1, 3, 5, 7, 9

A visual example where each group of dots increases by a constant quantity of $2$ dots.

Everyday Situations

Real-life contexts for sequences including financial planning, computer programming, schedules, and nature.