Find an algebraic expression which will produce the following sequence of numbers: {1, 2, 4, 8, 16, 64}

Expert Answers
mwmovr40 eNotes educator| Certified Educator

To do any problem in which you are asked to find an algebraic relationship between consecutive numbers one should start out by looking for simple numerical facts.  It helps immensely if you have a good grasp of "number sense" or if you practice basic number facts (also known as: multiplication tables!)

It should be noticed immediately that with the exception of the first number, the rest are all even numbers which means they are divisible by two.  We should then notice that

2x2 = 4

2x2x2 = 8

2x2x2x2 = 16  and so on up to the 64.

This should lead us to explore an exponential growth expression.  It helps to know that any number raised to the 0 power is = 1.  Therefore

2^0 = 1

2^1 = 2

2^2 = 4

2^3 = 8  and so on.

This gives us this algebraic relationship

y = 2^x  where x is a counting number from 0 to 6 inclusive.

 

hkj1385 eNotes educator| Certified Educator

The given sequence {1, 2, 4, 8, 16, 64} can be written in the form

1 = 2^0

2 = 2^1

4 = 2^2

8 = 2^3

16 = 2^4

32 = 2^5

64 = 2^6

Thus , the given sequence can be represented in the form

y = 2^n  ; where  'n' varies from 0 to 6

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