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Hi there.
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So for this problem, let's solve for a of this problem, which is about the geometric progression.
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A geometric progression known as gp is given such that the second term is 24 % of the zoom to infinity.
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Okay.
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So first of all, we are going to define the terms.
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The zoom to infinity of a gp is given by the following expression.
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The zoom to to infinity is a divided by one minus the rate for the magnitude of the rate less than one.
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Okay, the second term of the sequence, i art, given that the second term is 24 of the sum of to infinity, that will be that i are equals to 0 .24 times a divided by one minus the rate.
00:54
Okay, now solving in here, we will have that this is a times r times one minus r, equals to 0 .24 times a.
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Now, divided both sides by a in here, we will obtain that r times 1 minus r equals to 0 .24.
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Expanding this, this will give us r squared minus r plus 0 .24 equals to 0.
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So this is a quadratic equation, so we can use the quadratic formula.
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This is a quadratic expression, so we can use a quadratic formula to solve for this.
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And from this, we will obtain two possible solutions, 0 .6 and 0 .4.
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So these are the possible values of the common ratio, 0 .6 and 0 .4.
01:46
Now, for party b of this problem, we are asked about to solve this arithmetic progression.
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We are given two arithmetic progressions, p and q.
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We are told that p has first term a and common difference d while q has first term two times a plus one and common difference of d.
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So with that said for the fifth term in here we will have that the general formula for the nth term will be given by the following expression, a plus n minus 1, this times the.
02:45
Now for the fifth term, using this equation, we will obtain a plus four times the equals to 1...