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 the sequence 10, 20, 30, 40, ...?

Back

The common difference is 10.

Front

What is the explicit formula for the n-th term of the arithmetic sequence 2, 9, 16, 23, ...?

Back

a_n = 2 + 7(n-1) where a_n is the n-th term.

Front

How do you find the first term of an arithmetic sequence if you know the 14th term and the common difference?

Back

Use the formula a_n = a_1 + (n-1)d. Rearranging gives a_1 = a_n - (n-1)d.

Front

Is the sequence 78, 785, 7855, 78555, ... arithmetic?

Back

No, the sequence is not arithmetic because the differences between terms are not constant.

Front

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

Back

Use 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 25th term of the sequence if a_1 = 5 and d = 0.5?

Back

The 25th term is 17.

Front

What is the formula to find the common difference in an arithmetic sequence?

Back

The common difference d can be found using d = a_n - a_(n-1), where a_n and a_(n-1) are consecutive terms.

Front

If the first term of an arithmetic sequence is 14 and the common difference is 3, what is the 14th term?

Back

The 14th term is 43.

Front

What is the relationship between the first term, common difference, and the n-th term in an arithmetic sequence?

Back

The n-th term can be expressed as a_n = a_1 + (n-1)d.