Review sequences and series

Front

What is a sequence?

Back

A sequence is an ordered list of numbers that follow a specific pattern or rule.

Front

What is a series?

Back

A series is the sum of the terms of a sequence.

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 common difference in an arithmetic sequence?

Back

The common difference is the difference between consecutive terms in an arithmetic sequence.

Front

How do you calculate the sum of the first n terms of an arithmetic series?

Back

The sum can be calculated using the formula: S_n = n/2 * (a_1 + a_n), where S_n is the sum of the first n terms, a_1 is the first term, and a_n is the nth term.

Front

What is the formula for the sum of an arithmetic series?

Back

The formula is S_n = n/2 * (2a_1 + (n-1)d), where n is the number of terms, a_1 is the first term, and d is the common difference.

Front

Find the sum of the first 11 terms of the sequence 28, 34, 40, 46, 52, ..., 88.

Back

The sum is 638.

Front

What is the 22nd term of the sequence 5, 8, 11, ...?

Back

The 22nd term is 68.

Front

How many terms are in the sequence 28, 34, 40, ..., 88?

Back

There are 11 terms.

Front

What is the third term in the expansion of (x + 4)^5?

Back

The third term is 160 x^3.