Arithmetic Sequences

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

What is the common difference (d) in an arithmetic sequence?

Back

The common difference (d) is the fixed amount added to each term to get the next term in the sequence.

Front

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

Back

The nth term (a_n) 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 explicit formula for the arithmetic sequence: 3, 7, 11, 15...?

Back

a_n = 3 + 4(n - 1) where 4 is the common difference.

Front

Determine if the sequence 10, 20, 30, 40... is arithmetic.

Back

Yes, it is arithmetic with a common difference of 10.

Front

Find the 10th term of the arithmetic sequence: 2, 5, 8, 11...

Back

The 10th term is 29.

Front

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

Back

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

Front

If a_1 = 4 and d = 3, what is a_5?

Back

a_5 = 4 + 4(3) = 16.

Front

Is the sequence 1, 4, 9, 16... arithmetic?

Back

No, it is not arithmetic; it is a sequence of perfect squares.

Front

Write the explicit equation for the sequence: 12, 9, 6, 3...

Back

a_n = 12 - 3(n - 1).