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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

In mathematics, a continuo…

04:09

02:44

Identify the terms of each…

00:48

Write the first five terms…

00:14

Identify the like terms in…

00:35

Add the polynomials.$$…

00:33

Find the indicated term fo…

00:55

00:41

Combine the like terms.

00:23

01:48

00:27

Find the terms of the expr…

02:11

Use the given rule to writ…

02:02

Find the indicated term of…

00:21

02:01

01:15

Identify the first term an…

00:38

00:36

Find the first four terms …

00:50

Find a general term $a_{n}…

00:26

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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