Sequences and Series (Arithmetic and Geometric)

Front

What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is called the common difference.

Front

How do you find the nth term of an arithmetic sequence?

Back

The nth term (Tn) of an arithmetic sequence can be found using the formula: Tn = a + (n-1)d, where 'a' is the first term and 'd' is the common difference.

Front

What is a geometric sequence?

Back

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Front

How do you find the nth term of a geometric sequence?

Back

The nth term (Tn) of a geometric sequence can be found using the formula: Tn = a * r^(n-1), where 'a' is the first term and 'r' is the common ratio.

Front

What is the common difference in an arithmetic sequence?

Back

The common difference is the amount added to each term to get the next term in an arithmetic sequence.

Front

What is the common ratio in a geometric sequence?

Back

The common ratio is the factor by which each term in a geometric sequence is multiplied to obtain the next term.

Front

Find the first four terms of the arithmetic sequence with first term 76 and common difference -6.

Back

76, 70, 64, 58

Front

What is the next term in the sequence 11, 8, 5, 2?

Back

-1

Front

What is the value of r for the sequence 1/2, 1/4, 1/8, 1/16?

Back

1/2

Front

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

Back

68