Sequences — Quiz 5

Questions in this quiz (6)

1. What is the sum of the odd numbers from $$1$$ to $$101$$ inclusive?

   • 2051
   • 1052
   • 2601
   • 1967

2. Which of these is an equivalent explicit sequence to the recursive sequence $$a_1 = 4, \ a_n = 2a_{n-1}, \ n \geq 2$$?

   • $$2 \cdot 2^{n-1}$$
   • $$4 \cdot 2^{n-1}$$
   • $$2 \cdot 2^{n+1}$$
   • $$4 \cdot 2^{n}$$

3. If the sum of an infinite geometric series is $$81$$ and its common ratio is $$\frac{2}{3}$$, what is the fourth term in the series?

   • $$27$$
   • $$8$$
   • $$\frac{2}{3}$$
   • $$\frac{8}{27}$$

4. What is the sum of the terms of the geometric series:$$\frac{1}{4} + \frac{1}{16} + \frac{1}{64} +....?$$

   • $$\frac{1}{4}$$
   • $$\frac{1}{3}$$
   • $$\frac{3}{4}$$
   • $$\frac{4}{3}$$

5. The first term of a geometric sequence is 16, and the third term is 64. In terms of $$n$$, what is the $$n$$-th term of the sequence?

   • $$16\cdot (\frac{1}{2})^{n-1}$$
   • $$16\cdot (\frac{1}{4})^{n-1}$$
   • $$16\cdot (2)^{n-1}$$
   • $$16\cdot (\frac{1}{4})^n$$

6. In a certain geometric sequence, each term after the first is found by multiplying the previous term by a fixed positive integer. The sum of the first two terms of the sequence is 72. Which of the following values cannot be the first term of the geometric sequence?

   • $$9$$
   • $$12$$
   • $$16$$
   • $$24$$