Look at the table. Make a conjecture about the sum of the first 25 positive even numbers.

Mathematics

2 answers:

Nata [24]3 years ago

7 0

We notice that the sum is Σ= n(n+1),

Then the SUM of the first 25 even numbersis equal to 25(25+1) = 25 x 26

insens350 [35]3 years ago

6 0

Even number are of the form 2n. The sum of this sequence is the average of the first and last terms times the number of terms.

So the first term is 2 and the 25th term is 50 so the sum is:

(2+50)(25/2)

52*12.5=650

The conjecture they wish you to make is that for n terms, the sum will be:

s=n(n+1)

And for 25 terms that would give you:

s=25*26=650

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Jarvis left out a statement from the proof shown.which statement is best explained by the corresponding angles postulate

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The postulate of the corresponding angles establishes that when a transversal line cuts two parallel lines, the corresponding angles are congruent. These angles are on the same side of the parallel lines and on the same side of the transversal line.

Then, if we based on this definition and analize the figure attached, we can notice that the angles ∠1 and ∠3 are corresponding angles, so they are congruent. In this case the angle ∠1 is internal and the angle ∠3 is external.

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