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, known as the common difference.

Front

What is the formula for the nth term of an arithmetic sequence?

Back

The nth term (Tn) of an arithmetic sequence can be calculated using the formula: Tn = a + (n-1)d, where 'a' is the first term and 'd' is the common difference.

Front

What is the common difference in the sequence -7, -5, -3, -1, …?

Back

The common difference is 2.

Front

Which of the following is NOT an arithmetic sequence: 48, 24, 12, 6, 3, ...; 3, 7, 11, 15, 19, ...; 1, 0, -1, -2, -3, ...?

Back

48, 24, 12, 6, 3, ... is NOT an arithmetic sequence.

Front

What is the 6th term in the arithmetic sequence 18, 11, 4, …?

Back

The 6th term is -17.

Front

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

Back

The 7th term is 31.

Front

Define the term 'common difference' in an arithmetic sequence.

Back

The common difference is the constant amount that each term in the sequence increases or decreases by.

Front

What is an arithmetic series?

Back

An arithmetic series is the sum of the terms of an arithmetic sequence.

Front

How do you find 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 * (2a + (n-1)d), where 'a' is the first term and 'd' is the common difference.

Front

What is the difference between an arithmetic sequence and an arithmetic series?

Back

An arithmetic sequence is a list of numbers with a common difference, while an arithmetic series is the sum of the terms of that sequence.