Sequences Flashcard Review

Front

What is a common ratio in a geometric sequence?

Back

The common ratio (r) is the factor by which each term in a geometric sequence is multiplied to get the next term.

Front

How do you find the common ratio of the sequence -3, -6, -12, -24?

Back

Divide any term by the previous term: r = -6 / -3 = 2, -12 / -6 = 2, -24 / -12 = 2. The common ratio is r = -2.

Front

What is a common difference in an arithmetic sequence?

Back

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

Front

How do you find the common difference of the sequence 28, 228, 428, 628?

Back

Subtract any term from the next term: d = 228 - 28 = 200.

Front

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

Back

The nth term (a_n) can be found using the formula: a_n = a₁ + (n-1)d.

Front

Given a₁ = -28 and d = -2, find a₄₀.

Back

Using the formula: a₄₀ = -28 + (40-1)(-2) = -28 - 78 = -192.

Front

What are the next three terms in the sequence 6, 0, -6, -12?

Back

The common difference is -6. The next terms are -18, -24, -30.

Front

What is the first term of a sequence?

Back

The first term (a₁) is the initial value of the sequence from which all other terms are derived.

Front

What is a geometric sequence?

Back

A geometric sequence is a sequence 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 an arithmetic sequence?

Back

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