ID Sequences Flashcard

Front

Is the sequence arithmetic: -3, 3, -3, 3, ...?

Back

No, this sequence alternates between two values and does not have a common difference.

Front

Find the rule of the following sequence: 4, -16, 64, -256, ...

Back

The rule is a ratio of -4, meaning each term is multiplied by -4 to get the next term.

Front

What is the next term in the sequence: 14, 34, 54, 74, 94, ...?

Back

The next term is 114, as the sequence increases by 20 each time.

Front

Find the next three terms in the sequence: -33, -24, -15, -6, ...

Back

The next three terms are 3, 12, 21, as the sequence increases by 9 each time.

Front

What kind of sequence is the pattern 15, 17, 20, 24, 29, ...?

Back

This sequence is neither arithmetic nor geometric; it increases by varying amounts.

Front

Define an arithmetic sequence.

Back

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

Front

Define 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 difference in the arithmetic sequence 2, 5, 8, 11, ...?

Back

The common difference is 3, as each term increases by 3.

Front

How do you find the nth term of an arithmetic sequence?

Back

The nth term can be found using the formula: a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Front

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

Back

The nth term can be found using the formula: a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.