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In a certain sequence of numbers, each term after the first is found by doubling and then adding $3$ to the previous term. If the seventh term of the sequence is $125$, what is the first term?

 Jun 6, 2019
 #1
avatar+253 
+2

125-3=122

122/2=61

61-3=58

58/2=29
29-3=26
26/2=13
13-3=10
10/2=5
5-3=2
2/2=1
1-3=-2
-2/2=-1

 

Term 7: 125
Term 6: 61
Term 5: 29
Term 4: 13
Term 3: 5
Term 2: 1
Term 1:-1
The first term is -1

 Jun 6, 2019
 #2
avatar+103915 
+1

Probably easier ways to do this....but...let the first term  = a

 

So we have

 

a , (2a + 3) , (4a + 9) , (8a + 21), (16a + 45), (32a + 93), (64a + 189)

 

So

 

64a + 189  = 125

 

64 a  =  -64       divide both sides by -64

 

a  =  - 1

 

So  ....the sequence is

 

-1, 1, 5, 13, 29, 61, 125

 

 

cool cool cool

 Jun 7, 2019
 #3
avatar+103915 
+1

Nice, sinclairdragon.....you approached it from the other "end"  !!!!

 

 

cool cool cool

 Jun 7, 2019

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