To write the expression we could use for the nth term of the geometric sequence 3, 12, 48, 192 .... we would use a subscript 1 equals

Question

and r equals

Using that equation a subscript 12

Answer 1

 

The base formula for the nth term of a geometric sequence is:

 

   A_n = A₁ • r^n-1

 

    ... where n is the term of the sequence, r is the common ratio, and A₁ is the first term of the sequence

 

For this scenario,

   A₁ = 3 ... the first term

     r = 4 ... each term is 4 times the previous term

 

Plugging these in, we have the following equation:

 

   A_n = 3 • 4^n-1