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 (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 sum of the first n terms of an arithmetic series?

Back

The sum (S_n) of the first n terms of an arithmetic series 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 common difference in the sequence: 5, 8, 11, 14, ...?

Back

The common difference is 3.

Front

Determine if the sequence 10, 7, 4, 1, ... is arithmetic.

Back

Yes, the sequence is arithmetic with a common difference of -3.

Front

Find the 10th term of the arithmetic sequence where a_1 = 2 and d = 3.

Back

The 10th term is 29.

Front

What is the sum of the first 5 terms of the arithmetic series: 1, 3, 5, 7, 9?

Back

The sum is 25.

Front

Identify the common difference in the sequence: 20, 15, 10, 5, ...

Back

The common difference is -5.

Front

Is the sequence 4, 8, 12, 16, ... arithmetic?

Back

Yes, it is arithmetic with a common difference of 4.

Front

What is the 15th term of the arithmetic sequence where a_1 = 5 and d = 4?

Back

The 15th term is 61.