Math I Lab LT 16 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

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

Back

The common difference (d) is found by subtracting any term from the subsequent term: d = a(n+1) - a(n).

Front

Given the sequence: 5, 10, 15, 20, ..., what is the common difference?

Back

d = 5.

Front

What is the explicit formula for an arithmetic sequence?

Back

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

Front

Find the 10th term of the arithmetic sequence: 3, 7, 11, 15, ...

Back

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

Front

Is the sequence 2, 4, 6, 8, ... arithmetic?

Back

Yes, the common difference is 2.

Front

What is the 5th term of the sequence: 12, 9, 6, 3, ...?

Back

a_5 = 12 + (5-1)(-3) = 0.

Front

If the first term of an arithmetic sequence is 7 and the common difference is -2, what is the 4th term?

Back

a_4 = 7 + (4-1)(-2) = 1.

Front

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

Back

Yes, the common difference is -3.

Front

What is the formula to find the nth term of an arithmetic sequence?

Back

a_n = a_1 + (n-1)d.