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 explicit formula for an arithmetic sequence?

Back

The explicit formula is a_n = a_1 + (n-1)d.

Front

Given the sequence: 2, 5, 8, 11,... What is the common difference?

Back

The common difference is 3.

Front

If a_1 = 10 and d = -2, what is a_5?

Back

a_5 = 10 + (5-1)(-2) = 2.

Front

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

Back

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

Front

Given a sequence where a_1 = 4 and d = 3, what is the 10th term?

Back

a_10 = 4 + (10-1)3 = 31.

Front

Which of the following sequences is arithmetic: 1, 3, 5, 7 or 2, 4, 8, 16?

Back

1, 3, 5, 7 is an arithmetic sequence with a common difference of 2.

Front

What is the first term of the sequence defined by a_n = 7n - 2?

Back

The first term a_1 = 7(1) - 2 = 5.