Describe the relationship between the area of a parallelogram and the area of a triangle if they have the same base and the same
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1, a.) The two specific conjectures are in the first image.
1, b.) The two general conjectures are in the second image.
2, a.) Two specific conjectures for this pattern are:
- The common difference between two consecutive terms is 3.
- And the given difference is A.P.
2, b.) From our observation two general conjecture is that the given sequence is an arithmetic sequence and the common difference is 3.
For finding its nth term we can use the formula: a(n) = a + (n-1) x d.
2, c.) A formula for the given pattern is 5 + (n-1)3, where n is the number of the term.
We can check this by seeing if Pythagorean's theorem applies. The longest side is the hypotenuse, so let's see if this is true:
This is, indeed correct, thus, this <em>is </em><em>a right triangle.</em>
This is, indeed correct, thus, this <em>is </em><em>a right triangle.</em>