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Find the $20^{\text {th }}$ and $n^{\text {th }}$ terms of the G.P. $\frac{5}{2}, \frac{5}{4}, \frac{5}{8}, \ldots$
Precalculus
Chapter 9
Sequences and Series
Section 3
Series
Introduction to Sequences and Series
Campbell University
Piedmont College
Harvey Mudd College
Utica College
Lectures
07:16
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02:11
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02:02
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02:06
We have all the number one In this problem we need to find the 20th and then its term of NGP. So the given GPS five x 2 comma five x 4 05 x eight and so on. So first is definitely fight by two And the common ratio will be five x 4 divide by five x 2. So fight by four into 2 x five, one by two. So we have accommodation by two and first time in five by two. So we need to find We need to find 20 actor. So we have the formula that D. N. That is another term of an Ap No sorry, of G B equals two. Very general term of A G. P. Calls to A R. S. To the power and minus one. So let us write this A and itself a Address to the Power and -1. Okay, so if any is 20, A 20 will be equal to a R. S. To the power 19. So he is Fight by two in 2. One by two Raised to the Power 19. No, we have to just right this like A 20 equal to This will be 5-1 x 2-1 by tourists about 19. So two and 2 if a club will be getting fiber To raise to the Power 20. So this is 20th term and and this term and this term from here will be equal to a. N. Okay, that is five x 2 and 2 1 x two N minus one. So this is five into 1 x two into 1 x two raised to the power and -1. So if your club in if you club these two terms it will be fired by to raise to the parents. So these two word answers.
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