Arithmetic and 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 the 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 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 the sequence.

Front

How do you find 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.

Front

What is the formula to calculate the 10th term of the arithmetic sequence: 4, 7, 10, 13, 16?

Back

The 10th term is calculated as: a_10 = 4 + (10-1) * 3 = 31.

Front

If a tree grows by 3 cm every 3 days, what is the height after 12 days?

Back

After 12 days, the height will be: 2 + (12/3) * 3 = 14 cm.

Front

What is the common difference in the sequence: 4, 0, -4, -8, -12?

Back

The common difference is -4.

Front

How do you identify the common ratio in the sequence: 81, 27, 9, 3, 1?

Back

The common ratio is found by dividing any term by the previous term: 27/81 = 1/3.