True or false: If the sequence a, b, c text{ is arithmetic, then the sequence} 2a, 2b, 2c is geometric. Justify by giving example.

Write A if the sequence is arithmetic, G if it is geometric, H if it is harmonic, F if Fibonacci, and O if it is not one of the mentioned types. Show your Solution. a. $\frac{1}{3},\frac{2}{9},\frac{3}{27},\frac{4}{81},...$ b. $3,8,13,18,...,48$

Calculate: Polymomial equation with real coefficients taht has roots 3, 1 - i.

Arithmetic or Geometric?
a) If ${\displaystyle a_1,a_2,a_3,\cdots }$ is an arithmetic sequence, is the sequence ${\displaystyle a_1+2,a_2+2,a_3+2,\cdots }$ arithmetic?
b) If ${\displaystyle a_1,a_2,a_3,\cdots }$ is a geometric sequence, is the sequence ${\displaystyle 5a_1,5a_2,5a_3,\cdots }$ geometric?

What is -153 multiplied by -56?

What is 159 more than 956?

-8^10

DISCUSS DISCOVER: How Many Real Zeros Can a Polynomial Have? Give examples of polynomials that have the following properties, or explain why it is impossible to find such a polynomial.
(a) A polynomial of degree 3 that has no real zeros
(b) A polynomial of degree 4 that has no real zeros
(c) A polynomial of degree 3 that has three real zeros, only one of which is rational
(d) A polynomial of degree 4 that has four real zeros, none of which is rational
What must be true about the degree of a polynomial with integer coefficients if it has no real zeros?