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lilavasa [31]
3 years ago
10

Write an equation for the nth term of the geometric sequence 2, 8, 32, 128, ...

Mathematics
1 answer:
notka56 [123]3 years ago
6 0

Answer:

Equation: x(n)=2*4^(n-1)

a6=2048

Step-by-step explanation:

Take note that the common ratio is 4 because 2*4=8, 8*4=32, 32*4=128, and so on...

We will use the equation x(n) = ar^(n-1) where n represents the nth term, r stands for the common ratio, and "a" stands for the first term. We use (n-1) because ar^0 is for the 1st term

Given the first term is a=2, the common ratio is r=4, then we have the equation x(n)=2*4^(n-1)

So, 128*4=512 would be the 5th term, and the 6th term would be 512*4=2048

So a6=2048

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Another way could be:

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The first way I put it is simpler but if you really want to impress your teacher then I suggest going with the second way.

Also if you are looking to solve the equation then it would be:

3m - 4 = 14

      +4   +4

     ------------

       3m = 18

      -----    -----

         3        3

m = 5


Hope that helped :-)

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