Arithmetic & Geometric Sequences

Front

What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

Front

What is the common difference in an arithmetic sequence?

Back

The common difference is the fixed amount added to each term to get the next term in an arithmetic sequence.

Front

What is a geometric sequence?

Back

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Front

What is the common ratio in a geometric sequence?

Back

The common ratio is the factor by which we multiply each term to get the next term in a geometric sequence.

Front

Identify if the sequence is arithmetic, geometric, or neither: 4, 9, 14, 19, ...

Back

Arithmetic

Front

Identify if the sequence is arithmetic, geometric, or neither: 1, 3, 7, 13, ...

Back

Neither

Front

Identify if the sequence is arithmetic, geometric, or neither: 100, 50, 25, 12.5, ...

Back

Geometric

Front

Find the explicit formula for the sequence: 3, 6, 12, 24, ...

Back

aₙ = 3⋅2ⁿ ⁻ ¹

Front

What is the formula for the nth term of an arithmetic sequence?

Back

aₙ = a₁ + (n-1)d, where a₁ is the first term and d is the common difference.

Front

What is the formula for the nth term of a geometric sequence?

Back

aₙ = a₁ * r^(n-1), where a₁ is the first term and r is the common ratio.