LT

Test: Arithmetic and geometric progressions

This test develops recognition of arithmetic and geometric progressions and use of general-term formulas. Tasks include finding the common difference or ratio, determining missing terms and calculating sums of initial terms.

Question qty: 10
Duration in minutes: 14
Start »

Time left: 00:00:00

Finish the test
List of tests
Start over

Sample questions

  • The first two geometric-progression terms are a and b. Find q.
  • For a geometric progression b₁ = b, q = r. Find the sum of the first n terms.
  • Identify the sequence type: seka.
  • The first two arithmetic-progression terms are a and b. Find d.
  • How can arithmetic and geometric progressions be distinguished using adjacent terms?
  • For an arithmetic progression a₁ = a, d = d. Find a_n.
  • For an arithmetic progression a₁ = a, d = d. Find the sum of the first n terms.
  • For a geometric progression b₁ = b, q = r. Find b_n.

Arithmetic and geometric progressions

An arithmetic progression has constant difference d: aₙ = a₁ + (n − 1)d, and Sₙ = n(a₁ + aₙ)/2. A geometric progression has constant ratio q: bₙ = b₁qⁿ⁻¹.

Sums and models

For q ≠ 1, its finite sum is Sₙ = b₁(qⁿ − 1)/(q − 1). An infinite sum exists only when |q| < 1 and equals b₁/(1 − q). Distinguish a constant additive change from a constant multiplier before choosing the model.

Related mathematics tests

Rotation-angle trigonometry

This test explores angles of any magnitude and direction and their representation on the unit circle. Tasks cover coterminal-angle reduction, periodicity and the use of inverse trigonometric functions.

Solve: Rotation-angle trigonometry

Function properties and transformations

This test develops understanding of even and odd functions and common graph transformations. Students identify shifts, reflections and scaling and construct a new function formula from a given transformation.

Solve: Function properties and transformations

Logarithms and their properties

This test develops understanding of the definition of a logarithm and its relationship with exponents. Tasks apply product, quotient and power properties, transform expressions and check domain restrictions.

Solve: Logarithms and their properties

Trigonometric functions and equations

This test covers graphs, periods, ranges and signs of sine, cosine and tangent functions. Tasks also develop solution of elementary trigonometric equations and selection of solutions within a stated interval.

Solve: Trigonometric functions and equations