What is the sum of the geometric sequence 2,10,50... if there are 8 terms?
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Answer:
4. 158
Step-by-step explanation:
First let's make things a little simpler and put these arcs in terms of x. We know that the degree measure around the outside of a circle, regardless of its size, is 360. So let's say that arc BC is x. That means that arc BDC is 360 - x. This is because arc BC + arc BDC = 360. Substituting in our x's we have:
x + 360 - x = 360 and
360 = 360. (That's just the proof that putting in our x's as we did does in fact work!)
Following the formula then, we have
and
Multiply both sides by 2 to get rid of the fraction and get
44 = 360 - 2x
Subtract 360 rom both sides to get
-316 = -2x
Divide both sides by -2 to get that x = 158
Since we are looking for arc BC and we designated arc BC as our x, that means that arc BC = 158.
