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: 2, 5, 8, 11, what is the common difference?

Back

d = 3.

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

Front

Find a_10 in the arithmetic sequence: 4, 7, 10, 13, ...

Back

a_10 = 4 + (10-1)3 = 4 + 27 = 31.

Front

Is the sequence 10, 7, 4, 1 an arithmetic sequence?

Back

Yes, the common difference is -3.

Front

What is the common difference in the sequence: 15, 10, 5, 0, ...?

Back

d = -5.

Front

Find the next three terms in the arithmetic sequence: 12, 18, 24, ...

Back

30, 36, 42.

Front

If the first term of an arithmetic sequence is 5 and the common difference is 2, what is the 15th term?

Back

a_15 = 5 + (15-1)2 = 5 + 28 = 33.

Front

Determine if the sequence 8, 12, 16, 20 is arithmetic.

Back

Yes, the common difference is 4.