SOLUTION: Find the possible values of the common ration if the: (a) First term is 11 and the sum of the first 12 terms is 2922920 (b) first term is 1 and the sum of the first 6 terms is 1

Algebra ->  Sequences-and-series -> SOLUTION: Find the possible values of the common ration if the: (a) First term is 11 and the sum of the first 12 terms is 2922920 (b) first term is 1 and the sum of the first 6 terms is 1      Log On


   

Question 982268: Find the possible values of the common ration if the:
(a) First term is 11 and the sum of the first 12 terms is 2922920
(b) first term is 1 and the sum of the first 6 terms is 1.24994
Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
The only way to do these is by using technology, such as a TI-84 or similar calculator.

Instead of doing your problems for you, I'll do a couple that are
exactly like yours and you can do yours the same exact way.
I'm using a TI-84.

This one is like your first one

(a) First term is 13 and the sum of the first 10 terms is 4543825.
S%5Bn%5D%22%22=%22%22a%5B1%5D%28r%5En-1%29%2F%28r-1%29

S%5B10%5D%22%22=%22%2213%28r%5E10-1%29%2F%28r-1%29

4543825%22%22=%22%2213%28r%5E10-1%29%2F%28r-1%29

Press Y= and make it read like this:

\Y1=13(X^10-1)/(
X-1)
\Y2=4543825

Then press WINDOW and make it read

WINDOW
 Xmin=-10
 Xmax=10
 Xscl=1
 Ymin=-10
 Ymax=5000000      (Notice that I changed Ymax just larger than 4543825    
 Yscl=1
 Xres=1

Press GRAPH
Press 2ND TRACE
(choose 5 intersect)
Press ENTER 3 times

Read at bottom of screen X=4       Y=4543825

Answer:  r=4

You can do yours the same way.

-------------------------------------

This one is like your second one:

(b) first term is 2 and the sum of the first 7 terms is 2.856518
S%5Bn%5D%22%22=%22%22a%5B1%5D%28r%5En-1%29%2F%28r-1%29

S%5B7%5D%22%22=%22%222%28r%5E7-1%29%2F%28r-1%29

2.856518%22%22=%22%222%28r%5E7-1%29%2F%28r-1%29

Press Y= and make it read like this:

\Y1=2(X^7-1)/(
X-1)
\Y2=2.856518

You don't need to set the window, just reset the window
and graph by pressing ZOOM and selecting 6:ZStandard

Graph will show

Press 2ND TRACE
(choose 5 intersect)
Press ENTER 3 times

Read at bottom of screen X=.3       Y=2.856518

Answer:  r=0.3

You can do yours the same way. 
 
Edwin