Algebra Basics Quiz

Terminology in Algebra

• Coefficient: A number placed in front of a variable or term indicating how many times the variable is multiplied.
• Variable: A letter representing a number that can change or vary within an expression.
• Constant: A fixed numerical value that does not change, devoid of any variables.
• Expression: A mathematical phrase that includes numbers, variables, operators, and constants.
• Operator: The symbols denoting mathematical operations, such as addition, subtraction, multiplication, and division.
• Sequence: An ordered list of numbers or terms, following a specific rule.
• Terms: Individual elements or components within a sequence.

Sequences in Mathematics

• Arithmetic Sequence: A sequence generated by adding a common difference to the previous term, resulting in equal differences between consecutive terms.
• Formula for Arithmetic Sequence: ( A(n) = A(1) + (n - 1) d ), where:
  • ( A(n) ) = the nth term
  • ( A(1) ) = the first term
  • ( n ) = the term position
  • ( d ) = common difference.
• Common Difference: The fixed amount added to each term in an arithmetic sequence to reach the next term.

Geometric Sequences

• Geometric Sequence: A sequence where each term is found by multiplying the previous term by a constant non-zero multiplier.
• Formula for Geometric Sequence: ( A(n) = A(1) R^{(n-1)} ), with:
  • ( A(n) ) = the nth term
  • ( A(1) ) = the first term
  • ( R ) = common ratio (the fixed multiplier).

Special Sequences

• Fibonacci Sequence: A series where each term is the sum of the two preceding numbers, beginning with 0 and 1.
  • Example progression: 0, 1, 1, 2, 3, 5, 8, 13, ...
• Harmonic Sequence: A sequence where the reciprocals (1/n) of its terms form an arithmetic sequence.
  • Example: 1/2, 1/4, 1/6, 1/8, 1/10, ...

Division Terminology

• Quotient: The result obtained from dividing one number by another.
• Divisor: The number that divides the dividend in a division operation.
• Dividend: The number being divided, often represented within a division symbol.
• Remainder: The amount left over if division does not result in a whole number.
• Ratio: A comparison between two quantities, commonly expressed in the form of a fraction.