Arithmetic Sequences 2

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 explicit formula for an arithmetic sequence?

Back

The explicit formula is given by a_n = a_1 + (n-1)d, where a_1 is the first term, d is the common difference, and n is the term number.

Front

What is the recursive formula for an arithmetic sequence?

Back

The recursive formula is given by a_n = a_{n-1} + d, where d is the common difference.

Front

If the first term of an arithmetic sequence is 5 and the common difference is 3, what is the 4th term?

Back

The 4th term is 5 + (4-1) * 3 = 14.

Front

How do you find the common difference in an arithmetic sequence?

Back

The common difference (d) can be found by subtracting any term from the subsequent term: d = a_{n} - a_{n-1}.

Front

What is the 10th term of the sequence 2, 5, 8, 11...?

Back

The 10th term is 2 + (10-1) * 3 = 29.

Front

What does it mean if the common difference is negative in an arithmetic sequence?

Back

If the common difference is negative, the terms of the sequence decrease as you move from one term to the next.

Front

Write the recursive formula for the sequence 4, 7, 10, 13...

Back

a_n = a_{n-1} + 3, a_1 = 4.

Front

What is the explicit formula for the sequence 1, 4, 7, 10...?

Back

a_n = 1 + (n-1) * 3.

Front

If a_1 = 10 and d = -2, what is a_5?

Back

a_5 = 10 + (5-1)(-2) = 2.