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In the sequence                           1, 2, 2, 4, 8, 32, 256...,

each term (starting from the third term) is the product of the two terms before it. For example, the seventh term is 256, which is the product of the fifth term (8) and the sixth term (32).

This sequence can be continued forever, though the numbers very quickly grow enormous! (For example, the 14th  term is close to some estimates of the number of particles in the observable universe.)

What is the last digit of the 35th term of the sequence?

SmartMathMan  Jan 19, 2018
edited by SmartMathMan  Jan 19, 2018
 #1
avatar+87569 
+1

Last digit pattern

 

Term            Last Digit

3                    2

4                    4

5                    8 

6                    2 

7                    6

8                    2

9                    2 

10                  4

11                  8 

12                  2

13                  6

14                  2          

 

The  pattern has a repeating length of  6

 

And  35  =   6n +  5

 

So.... the 35th term has the same last digit as the 5th term  =   8

 

 

cool cool cool

CPhill  Jan 19, 2018

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