Arithmetic Sequences--Short

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 to the next term in the sequence.

Front

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

Back

5, 8, 11, 14, 17

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 the arithmetic sequence 2, 5, 8, 11?

Back

The explicit formula is a_n = 2 + (n - 1)3.

Front

Determine if the sequence 4, 10, 16, 22 is arithmetic.

Back

Yes, it is arithmetic with a common difference of 6.

Front

What is the next term in the arithmetic sequence 12, 15, 18?

Back

The next term is 21.

Front

If an arithmetic sequence has a first term of 10 and a common difference of -2, what is the 6th term?

Back

The 6th term is 10 + (6 - 1)(-2) = 0.

Front

How do you calculate 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), where S_n is the sum of the first n terms.

Front

What is the sum of the first 5 terms of the arithmetic sequence 3, 7, 11, 15?

Back

The sum is 3 + 7 + 11 + 15 + 19 = 55.