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 (d) in an arithmetic sequence?

Back

The common difference (d) is the fixed amount that each term increases or decreases by in an arithmetic 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 formula to find the sum of the first n terms of an arithmetic sequence?

Back

The sum of the first n terms (S_n) is given by the formula: S_n = n/2 * (a_1 + a_n), where a_n is the nth term.

Front

Find the common difference in the sequence: 5, 10, 15, 20, ...

Back

d = 5

Front

Find the next three terms in the arithmetic sequence: 2, 5, 8, 11, ...

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14, 17, 20

Front

What is the 10th term in the arithmetic sequence: 3, 7, 11, 15, ...

Back

The 10th term is 39.

Front

If the first term of an arithmetic sequence is 4 and the common difference is 3, what is the 5th term?

Back

The 5th term is 16.

Front

Find the common difference in the sequence: -10, -7, -4, -1, ...

Back

d = 3

Front

What is the 20th term in the arithmetic sequence: 1, 4, 7, 10, ...

Back

The 20th term is 58.