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 in an arithmetic sequence?

Back

The common difference (d) is the constant amount that each term in the sequence increases or decreases by.

Front

Find the common difference in the sequence: 5, 8, 11, 14, ...

Back

d = 3

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

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

Back

a_10 = 2 + (10-1)3 = 29

Front

Is the sequence 4, 7, 10, 13, ... arithmetic?

Back

Yes, it is arithmetic with a common difference of 3.

Front

Determine if the sequence 1, 2, 4, 8, ... is arithmetic.

Back

No, it is not arithmetic because the differences are not constant.

Front

What is the formula for 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

Find the sum of the first 5 terms of the arithmetic sequence: 3, 6, 9, 12, ...

Back

S_5 = 5/2 * (3 + 15) = 45

Front

What is the 5th term in the arithmetic sequence: -10, -7, -4, -1, ...

Back

a_5 = -10 + (5-1)3 = 2