Arithmetic Sequence and Series (11.2)

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 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

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

What is the formula for the sum of the first n terms of an arithmetic series?

Back

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

Front

Given a_1=5 and a_2=11, find a_15.

Back

a_15 = 5 + (15-1)(11-5) = 89.

Front

Find the 22nd term of the sequence: 5, 8, 11, ...

Back

a_22 = 5 + (22-1)(8-5) = 68.

Front

Identify the common difference in the sequence: 97, 86, 75, 64, ...

Back

The common difference is -11.

Front

What are the next two terms of the sequence 4, 7, 10, 13?

Back

The next two terms are 16 and 19.

Front

Find the sum of the arithmetic series: 2 + (-2) + (-6) + (-10)..., S_10.

Back

S_10 = -160.

Front

What is the first term of an arithmetic sequence?

Back

The first term (a_1) is the initial term of the sequence from which all other terms are derived.