Arithmetic Sequence

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 the formula for the sum of the first n terms of an arithmetic sequence?

Back

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

Front

Find the 10th term of the arithmetic sequence: 3, 7, 11, ...

Back

The 10th term is 39.

Front

Determine if the sequence 5, 10, 15, 20, ... is arithmetic.

Back

Yes, it is an arithmetic sequence with a common difference of 5.

Front

What is the common difference of the sequence: 12, 8, 4, 0, ...?

Back

The common difference is -4.

Front

Write the recursive rule for the arithmetic sequence: 10, 7, 4, 1, ...

Back

a_1 = 10; a_n = a_{n-1} - 3.

Front

Find the 15th term of the arithmetic sequence: -2, 1, 4, 7, ...

Back

The 15th term is 40.

Front

What is the first term of the arithmetic sequence if the 5th term is 20 and the common difference is 4?

Back

The first term is 8.