1. ## Math problems

I have these problems

1. Use inductive reasoning to determine the next three numbers in the pattern: 2, 9, 20, 35, ….
2. Find a counterexample to the statement “The square of a number added to the sum of the number and five is a prime number”

3 Estimate the area of the triangle in square units. Each square represents 1 square unit.

2. Originally Posted by Amy
I have these problems

1. Use inductive reasoning to determine the next three numbers in the pattern: 2, 9, 20, 35, ….
look at the pattern of differences, the differences are 7, 11, 15. Now look at the differences for this sequence, they are 4, 4.

So using incomplete induction we assume that this pattern will hold and the next term in the sequence of first differences is 19, and so the next term in the original sequence is 44.

RonL

3. Originally Posted by Amy
2. Find a counterexample to the statement “The square of a number added to the sum of the number and five is a prime number”
This is: find a counter example to $\displaystyle N=n^2+n+5$ is a prime.

Try $\displaystyle n=1, 2, 3, ..$ untill you find an $\displaystyle N$ which is non-prime. You won't have to look far.

RonL

4. Hello, Amy!

3) Estimate the area of the triangle in square units.
Each square represents 1 square unit.

Consider the circumscribing rectangle.
. . It has an area of: .$\displaystyle 4 \times 2 \:=\: 8$ units˛.

Now find the areas of the three right triangles.
. . $\displaystyle \begin{array}{cccc}\text{Upper-left:} & \frac{1}{2}(4)(1) & = & 2 \\ \text{Lower-left:} & \frac{1}{2}(3)(1) & = & 1.5 \\ \text{Lower-right:} & \frac{1}{2}(1)(2) & = & 1 \end{array}\qquad\text{Total: }4.5$ units˛

Therefore, the area of the triangle is: .$\displaystyle 8 - 4.5 \;=\;3.5$ units˛.