Arithmetic Sequences and Series

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 the next term in the 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 for the sum of the first n terms of an arithmetic series?

Back

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

Front

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

Back

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

Front

What is the 7th term in the sequence 7, 11, 15, ...?

Back

The 7th term is 31.

Front

How do you determine the sum of an arithmetic series written in Sigma Notation?

Back

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

Front

Find the next three terms in the arithmetic sequence: -3, -8, -13, -18, ...

Back

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

Front

What is the common difference in the sequence 7, 11, 15, ...?

Back

The common difference is 4.

Front

What does Sigma Notation represent in arithmetic series?

Back

Sigma Notation is a concise way to represent the sum of a sequence of numbers.