Sequences and series applications and problems.

1. Given a geometric sequence in which and , what is the value of ?

2. If the third term of a geometric sequence is 36 and the eighth term is 8748, find
the first term.

3. Given the geometric sequence in which and r = , which term has a
value of 27?

4. Find the value of:

5. Find the value of:

6. Find the sum of the infinite geometric sequence 4, 16, 64, ...

7. An equilateral triangle with each side 14 cm long is
formed. The midpoints of the sides are joined to form
another equilateral triangle and the midpoints of this
triangle are joined to form still another triangle. If this
process is continued indefinitely, what is the sum of the
perimeters of the triangles formed?

8. Write the following series in sigma notation: 1 + 5 + 25 + 125 + 625

9. It is said that during the last weeks of his life, Abraham deMoivre needed 15
minutes more sleep each night, and when he needed 24 hours of sleep he
would die. If he needed 8 hours sleep on September 1, what day did he die?
Abraham on Wikipedia