Arithmetic Sequences Review

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

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

Back

The nth term (a_n) of an arithmetic sequence 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 common difference in the sequence: 2, 5, 8, 11, ...?

Back

The common difference is 3, as each term increases by 3.

Front

If a_1 = 10 and d = 4, what is a_5?

Back

a_5 = 10 + (5-1)4 = 10 + 16 = 26.

Front

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

Back

The sum (S_n) of the first n terms can be calculated using the formula: S_n = n/2 * (a_1 + a_n), where a_n is the nth term.

Front

Find the 10th term of the arithmetic sequence: 3, 7, 11, ...

Back

a_10 = 3 + (10-1)4 = 3 + 36 = 39.

Front

What is the first term of the arithmetic sequence if a_14 = 68 and d = 3?

Back

a_1 = a_14 - (14-1)d = 68 - 39 = 29.

Front

In the sequence 1, 4, 7, 10, ..., what is the 20th term?

Back

a_20 = 1 + (20-1)3 = 1 + 57 = 58.

Front

If Jerry deposits $20,000 and earns $1,750 each year, how much will he have after 8 years?

Back

Total amount after 8 years = $20,000 + (8 * $1,750) = $20,000 + $14,000 = $34,000.

Front

What is the explicit formula for the arithmetic sequence defined by a_n = 5 + (n-1)6?

Back

The explicit formula can be simplified to a_n = 6n - 1.