Exam 13: Sequences

This problem gives some information about a specific geometric progression. .

Find the ninth term in the expansion of .

Find the fraction form for

Consider the following finite series: For which values of i does the following summation notation hold true? must range from __________ to __________ .

Solve the equation for

Write the first five terms of the sequence defined by the recursion formula.

Assume that a thin sheet of paper is 0.005 inch thick. The paper is torn in half, and the two halves placed together. The pile of paper is torn in half again, and then the two halves placed together and torn in half again. The paper is large enough so this process may be performed a total of 5 times. How thick is the pile of torn paper?

This problem gives some information about a specific geometric progression. .

Write the first five terms of the sequence with the following general term.

Any repeating, nonterminating decimal may be viewed as a series. For instance, Write the following fraction as a series.

Any repeating, nonterminating decimal may be viewed as a series. For instance, . Use this fact to express the following series as a fraction.

Write the first five terms of the sequence defined by the recursion formula.

After 1 day, a colony of 40 bacteria reproduces to become 200 bacteria. After 2 days, they reproduce to become 1,000 bacteria. If they continue to reproduce at this rate, how many bacteria will be present after 6 days? __________ bacteria

Write the first three terms of the expansion of .

Expand and simplify.

Find the sum of the following geometric series.

Find the sum of the following geometric series.

Write the first five terms of the sequence defined by the recursion formula.

Write the first five terms of the sequence defined by the recursion formula.

Find the sum of the following geometric series.