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 an arithmetic sequence?

Back

The common difference 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, d is the common difference, and n is the term number.

Front

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

Back

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

Front

Find the 35th term in the arithmetic sequence: -10, -14, -18, -22.

Back

The 35th term is -146.

Front

What is the common difference in the sequence: -34, -29, -24, -19?

Back

The common difference is d = 5.

Front

Find the next three terms in the arithmetic sequence: -33, -24, -15, -6.

Back

The next three terms are 3, 12, 21.

Front

Is the sequence 17, 9, 1, -7 an arithmetic sequence?

Back

Yes, the sequence is arithmetic because the differences between consecutive terms are constant.

Front

What is the formula for 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, a_1 is the first term, and a_n is the nth term.

Front

If the first term of an arithmetic sequence is 5 and the common difference is 3, what is the 10th term?

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The 10th term is 32.