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

Define the common difference in an arithmetic sequence.

Back

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

Front

If a₁ = 5 and a₂ = 11, what is the common difference?

Back

The common difference is 6 (11 - 5).

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 = a₁ + (n-1)d, where d is the common difference.

Front

Find the 15th term of the sequence where a₁ = 5 and d = 6.

Back

a₁₅ = 5 + (15-1)6 = 89.

Front

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

Back

The 7th term is 31.

Front

Identify the next term in the sequence 2, 4, 8, 16.

Back

The next term is 32.

Front

What is the common difference in the sequence 97, 86, 75, 64, ...?

Back

The common difference is -11.

Front

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

Back

The common difference is 2.

Front

How do you find the sum of the first n terms of an arithmetic series?

Back

The sum (S_n) can be calculated using the formula: S_n = n/2 * (a₁ + a_n), where a_n is the nth term.