Find the following nth term 3,15,75,375,1875

Question

It is hard

Answer 1

Hi,

First identify if the sequence.

Arithmetic (a sequence where consecutive terms differ by a common difference) or

Geometric (a sequence where each term is multiplied by a common ratio to get the subsequent term.)

 

3,15,75,375,1875

 

Each term is 5 times the previous term.

That is, 3·5=15

    15·5=75

  75·5=375

and so on.

Therefore, r, the common ratio is 5. 

Second use the Geometric Explicit Formula, 

a_n= a₁r^(n-1), where a₁ is the first term,

And, write an expression for the nth term, a_n.

 

a_n=3·5^(n-1)

Answer 2

Hello, Eugene,

     What you are showing me is called a Geometric Sequence.  This means that the number that comes after the first number is multiplied by some number.  I will show you how it works from an example just like yours:

 

4, 12, 36, 108, 324      What number do you multiply "4" by to get 12?    3  (common ratio)   Now check it out.

 

4x3,  12x3, 36x3, 108 x3        By multiplying each term by "3," I got the rest of the numbers in the sequence.

 

I will let you do your problem.  I hope my example helps you to work yours!  Susan C.