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

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

Given the sequence 3, 7, 11, ..., what is the common difference?

Back

The common difference is 4.

Front

What is the explicit formula for the arithmetic sequence 2, 5, 8, ...?

Back

The explicit formula is a_n = 2 + 3(n-1).

Front

Find the 10th term of the arithmetic sequence: 4, 9, 14, ...

Back

The 10th term is 49.

Front

If the first term of an arithmetic sequence is 10 and the common difference is 5, what is the 5th term?

Back

The 5th term is 30.

Front

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

Back

The sum S_n = n/2 * (a_1 + a_n), where a_1 is the first term and a_n is the nth term.

Front

Given the arithmetic sequence: 1, 4, 7, ..., what is the 15th term?

Back

The 15th term is 43.

Front

How do you derive the explicit formula from the sequence: 6, 10, 14, ...?

Back

The explicit formula is a_n = 6 + 4(n-1).