Arithmetic 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

If the first term of an arithmetic sequence is 5 and the common difference is 3, what are the first five terms?

Back

5, 8, 11, 14, 17

Front

How do you find the n^th term of an arithmetic sequence?

Back

The n^th term can be found using the formula: a_n = a₁ + (n-1)d, where a₁ is the first term and d is the common difference.

Front

What is the explicit formula for the n^th term of the sequence 4, 7, 10, 13, ...?

Back

a_n = 4 + (n-1)3 = 3n + 1.

Front

What is the 10^th term of the arithmetic sequence 2, 5, 8, 11, ...?

Back

The 10^th term is 29.

Front

If the first term of an arithmetic sequence is 12 and the common difference is -2, what is the 6^th term?

Back

The 6^th term is 0.

Front

What is the sum of the first n terms of an arithmetic sequence?

Back

The sum can be calculated using the formula: S_n = n/2 * (a₁ + a_n), where S_n is the sum of the first n terms.

Front

What is the common difference of the sequence 10, 7, 4, 1, ...?

Back

The common difference is -3.

Front

If an arithmetic sequence has a common difference of 5 and the first term is 3, what is the 20^th term?

Back

The 20^th term is 98.