Arithmetic Sequences and Series Practice

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 formula for the nth term of an arithmetic sequence?

Back

The nth term (a_n) can be calculated using the formula: a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Front

How do you find the common difference in an arithmetic sequence?

Back

The common difference (d) is found by subtracting any term from the subsequent term: d = a_(n+1) - a_n.

Front

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

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_n is the nth term.

Front

What is the 14th term of the sequence: 7, 2, -3, ...?

Back

The 14th term is -357.

Front

What is the next term in the sequence: 2, 4, 8, 16?

Back

The next term is 32.

Front

How do you evaluate the sum of an arithmetic series?

Back

To evaluate the sum, identify the first term, last term, and number of terms, then apply the sum formula.

Front

What is the 26th term in the arithmetic sequence: 20, 26, 32, 38, ...?

Back

The 26th term is 170.

Front

What are the next three terms in the sequence: -3, -8, -13, -18?

Back

The next three terms are -23, -28, -33.

Front

What is the sum of the series: 0, -7, -14, -21, ... up to 17 terms?

Back

The sum S_17 is -952.