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avatar+2509 

Help 14,15,16

NotSoSmart  May 16, 2018
 #1
avatar+87334 
+1

14

 

We have the following  [geometric ] pattern

 

22,  17.6 , 14.08

 

The common ratio  is     17.6 / 22   = 4/5

 

So.....we want to find this

 

22(4/5)^n  = 10

 

(4/5)^n  = 10/22

 

(4/5)^n  = 5/11      take the log of both sides

 

log (4/5)^n  = log (5/11)

 

n * log (4/5)  = log (5/11)

 

n =  log (5/11)  / log (4/5)  ≈  3.5

 

Thus...we need to round this up to 4

 

So....the 4th square will have a side length of  < 10  inches

 

 

cool cool cool

CPhill  May 16, 2018
 #2
avatar+87334 
0

15

 

50th term of   -2, 4, 8 , 14

 

This is an arithmetic series with a  common difference  of 6

 

So....the 50 th term is

 

-4  + 6 (49)   =

 

290

 

 

cool cool cool

CPhill  May 16, 2018
 #3
avatar+87334 
+1

16

 

20th  term of 

 

-2   4  -8    16

 

This is a geometric series where the nth term can be represented as

 

(-2)^n

 

So....the 20 th   term is

 

(-2)^20  =

 

1048576

 

 

 

cool cool cool

CPhill  May 16, 2018

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