Arithmetic Sequences1

Front

What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is called the common difference.

Front

What is the common difference in the sequence 13, 19, 25, ...?

Back

The common difference is 6, calculated as 19 - 13 or 25 - 19.

Front

How do you find the nth term of an arithmetic sequence?

Back

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

Front

What is the 6th term in the arithmetic sequence 13, 19, 25, ...?

Back

The 6th term is 43, calculated as \( 13 + (6-1) \cdot 6 = 43 \).

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What is the next term in the sequence 13, 19, 25, ...?

Back

The next term is 31, calculated as \( 25 + 6 = 31 \).

Front

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

Back

The 10th term is 32, calculated as \( 5 + (10-1) \cdot 3 = 32 \).

Front

What is the formula for the sum of the first n terms of an arithmetic sequence?

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The sum \( S_n \) of the first n terms can be calculated using the formula: \( S_n = \frac{n}{2} \cdot (a_1 + a_n) \) or \( S_n = \frac{n}{2} \cdot (2a_1 + (n-1)d) \).

Front

What is the 4th term in the arithmetic sequence 2, 5, 8, ...?

Back

The 4th term is 11, calculated as \( 2 + (4-1) \cdot 3 = 11 \).

Front

How do you determine if a sequence is arithmetic?

Back

A sequence is arithmetic if the difference between consecutive terms is constant.

Front

What is the common difference in the sequence 7, 10, 13, ...?

Back

The common difference is 3, calculated as 10 - 7 or 13 - 10.