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Find a G.P. for which sum of the first two terms is $-4$ and the fifth term is 4 times the third term.

Precalculus

Chapter 9

Sequences and Series

Section 3

Series

Introduction to Sequences and Series

Johns Hopkins University

Oregon State University

University of Michigan - Ann Arbor

Idaho State University

Lectures

07:16

In mathematics, a continuo…

04:09

01:33

Find each sum.$$\b…

00:58

Find the sum of the first …

00:32

00:15

01:26

Find the indicated part of…

02:39

01:17

Find a general term $a_{n}…

01:10

write the first four terms…

00:42

Write the first four terms…

01:25

00:22

00:40

Find the general term of a…

01:31

Write the first five terms…

01:22

00:59

00:56

00:26

01:05

00:38

01:06

Hello. We have problem number 16 in which we have to find A G. P. For which some of the first two terms is minus four. So some of the first two terms is minus four. So let the J. P E G P B. A. They are yeah Squire, A R. Q and so on. So we have some of first two terms. So a place A plus sorry, A plus A. R. Equal to um minus four. And the fifth term is four times the third term. The fifth time will be are raised powerful. So fifth term they are is the powerful aid is four times the third time. That is air square. Air square. So a and they will get again slow. So we'll be getting artificially power four minus four. R squared equal to zero which means our square are square minus for equal to zero. So either are equal to zero which is not possible odd. Are equal to plus minus two. Okay so are equal to plus minus two? No infrequent, just like this life. Okay, so if we take are equal to plus two, we will be getting from here. A one plus are equal to minus four. So A will be equal to minus four by one plus. Are so minus four by a tool +13 So this is the first time. Okay, so G P will be equal to in this case it will be a minus four by three into a ar minus eight by three. He had a squared, yeah squared minus 16 by three and so on. This is one of the G. P. Then I called you too. Now when I call to minus two we will be getting a call to minus four buyer one plus. R Mine is fall by mine as well noted for so in this case it will be minus four. Yeah minus 16. Okay. I was four minus Okay. I was minus two. Yes. So mine's for into two in his report is four. So for an A. R minus eight A r squared, um, 16 and so on. So there are two possible GPS. Thank you.

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