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The sum of the terms of a geometric sequence is called a geometric _____. The sum of the terms of an infinite geometric sequence is called an _____ geometric series.

Fill in the blanks. \(5,15,25,35,45,55, \dots\) is an example of an ___________ sequence. The first __________ is 5 and the common _________ is 10.

Fill in the blanks. In the notation \(\sum_{k=1}^{5}(2 k-5), k\) is called the ____________ of summation.

Fill in the blanks. The exponent on \(a\) in the fourth term of the expansion of \((a+b)^{6}\) is ____ and the exponent on \(b\) is ____.

Evaluate each expression. See Examples 3 and 4. $$ 6 ! $$

Write the first five terms of each arithmetic sequence with the given properties and find the specified term. First term: \(7,\) common difference: \(12 ;\) find the 30th term.

Write the first five terms of the arithmetic sequence with the following properties. The first term is 4 and the sixth term is 39.

Find the sum of each infinite geometric series, if possible. See Examples 7 and 8. $$ 12+6+3+\cdots $$

Insert the given number of arithmetic means between the numbers. Three arithmetic means between 20 and 30

Insert the given number of arithmetic means between the numbers. Two arithmetic means between 10 and 19