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 constant amount that each term in the sequence increases or decreases by.

Front

Find the common difference: 2, 5, 8, 11, ...

Back

d = 3

Front

Is the sequence arithmetic: 4, 8, 12, 16, ...?

Back

Yes

Front

Is the sequence arithmetic: 1, 2, 4, 8, ...?

Back

No

Front

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

Back

The 10th term is 39.

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 5th term of the sequence: 10, 15, 20, ...

Back

The 5th term is 30.

Front

If the first term is 5 and the common difference is 2, what is the 15th term?

Back

The 15th term is 33.

Front

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

Back

The sum (S_n) can be calculated using the formula: S_n = n/2 * (a_1 + a_n), where a_n is the nth term.