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.

Test your understanding of fundamental algebra concepts including coefficients, variables, constants, and expressions. This quiz also covers arithmetic sequences and the formula used to calculate them. Perfect for reinforcing your knowledge in introductory algebra topics!