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 (d) is the constant amount that each term increases or decreases by in an arithmetic sequence.

Front

How do you find the common difference in a sequence?

Back

To find the common difference, subtract the first term from the second term (d = a2 - a1).

Front

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

Back

The second term is 8 (5 + 3).

Front

What is the formula for the nth term of an arithmetic sequence?

Back

The nth term (an) can be calculated using the formula: an = a1 + (n-1)d, where a1 is the first term and d is the common difference.

Front

Find the 10th term of the arithmetic sequence 4, 7, 10, 13, ...

Back

The 10th term is 34.

Front

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

Back

The common difference is -3.

Front

If the common difference of an arithmetic sequence is 2 and the first term is 1, what is the 5th term?

Back

The 5th term is 9.

Front

How do you determine the number of terms in an arithmetic sequence?

Back

You can determine the number of terms by rearranging the nth term formula: n = (an - a1)/d + 1.

Front

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

Back

The sum (S) can be calculated using the formula: S = n/2 * (a1 + an).