Arithmetic and Geometric Sequences and Series Review

Front

What is an arithmetic sequence?

Back

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

Front

How do you find the common difference in an arithmetic sequence?

Back

The common difference (d) can be found by subtracting any term from the subsequent term: d = a(n+1) - a(n).

Front

Given the sequence 2, 8, 14, 20, 26, what is the common difference?

Back

The common difference is 6.

Front

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

Back

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

Front

Find the next four terms of the arithmetic sequence 16, 24, 32,...

Back

The next four terms are 40, 48, 56, 64.

Front

What is the eleventh term of an arithmetic sequence where a1 = 3 and d = 6?

Back

The eleventh term is 63.

Front

Determine the common difference for the arithmetic sequence 9, 16, 23, 30,...

Back

The common difference is 7.

Front

What does the symbol ∑ represent in mathematics?

Back

The symbol ∑ represents the summation operator, which is used to sum a sequence of numbers.

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

How do you find the common ratio in a geometric sequence?

Back

The common ratio (r) can be found by dividing any term by the previous term: r = a(n) / a(n-1).