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

How do you find the nth term of an arithmetic sequence?

Back

The nth term (a_n) of an arithmetic sequence 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 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 can you determine if a sequence is arithmetic?

Back

To determine if a sequence is arithmetic, check if the difference between consecutive terms is the same throughout the sequence.

Front

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

Back

The common difference (d) can be calculated using the formula: 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 5 and the common difference is 3, what is the 10th term?

Back

The 10th term can be found using the formula: a_10 = 5 + (10-1)3 = 5 + 27 = 32.

Front

What is the 26th term of the arithmetic sequence: 2, 4, 6, 8, ...?

Back

The 26th term is a_26 = 2 + (26-1)2 = 2 + 50 = 52.

Front

How do you find the sum of the first n terms of an arithmetic sequence?

Back

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

Front

What is the sum of the first 10 terms of the arithmetic sequence: 1, 3, 5, 7, ...?

Back

The sum is S_10 = 10/2 * (1 + 19) = 5 * 20 = 100.

Front

If the 5th term of an arithmetic sequence is 20 and the common difference is 4, what is the first term?

Back

The first term can be found using the formula: a_1 = a_5 - (5-1)d = 20 - 16 = 4.