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1. What is the sum of the first 7 terms of the series −4+8−16+32−...?

 

2. What is the sum of the series?

4+12+36+108+...+8748

 

3. A car dealership sold one car in its first month of business. The number of cars it sold doubled each month. What was the total number of cars the dealership sold during the first 12 months?

 

4. Michaela drops a ball vertically from a height of 80 feet. The peak height after each bounce is half the previous height.

How far does the ball travel from the time she drops it until it reaches the peak height after the 5th bounce?

jbouyer  Mar 1, 2018
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2+0 Answers

 #1
avatar+86528 
+2

1.  -4 + 8 - 16 + 32 - 64 + 128 - 256   =

 

(-4 + 8)  + (-16 + 32) + (-64 + 128)  - 256  =

 

4  +  16  + 64 -  256  =

 

84  -  256  =

 

-172

 

Second one

 

4 + 12 +  36   +  108  +  .....+  8748

 

We need to find what term the last is

 

We can solve this

 

4*3^(n-1)  =  8748    divide both sides by 4

 

3^(n - 1)  =   2187      take the log of both sides

 

log 3^(n- 1)  =  log 2187     and we can write

 

(n - 1) log 3  = log 2187      divide both sides by log 3

 

(n - 1)  =   log 2187  / log 3

 

n - 1  =  7    add 1 to both sides

 

n  = 8

 

The sum is given by

 

4 ( 1 - 3^8) / ( 1 - 3)   = 13,120

 

 

cool cool cool

CPhill  Mar 1, 2018
 #2
avatar+86528 
+2

Third one

 

We have 

 

1 + 2 + 4 + .....+ 2^(n - 1)

 

The sum  is

 

1 ( 1 - 2^12)  / ( 1 - 2)   =    4095  cars

 

 

Last one

 

The total distance  traveled in the first 5 bounces is

 

80 + 80  ( 1 - (1/2)^(5 - 1) ) / ( 1 - 1/2)    = 230 ft

 

And the distance traveled from  the 5th bounce to the next peak is  80 (1/2)^5 =  2.5 ft

     

So...the total distance traveled is  230  + 2.5  =   232.5 ft

 

 

cool cool cool

CPhill  Mar 1, 2018

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