How do I find the nth term in the sequence 7, 14, 28, 56, 112

Question

Help I’m so confused!!

Answer 1

a(n)=(a)(r)^(n-1) where a=1st term and r=common ratio

a(1)=(7)(2)^(1-1)=7*2⁰=7*1=7

a(2)=(7)(2)^(2-1)=7*2=14

a(3)=(7)(2)^(3-1)=7*2²=7*4=28

a(4)=(7)(2)^(4-1)=7*2³=7*8=56

and so on

Answer 2

This is a Geometric Sequence.  The common ratio (r) is 2.  That is, each term is 2 times the previous term.  The first term is 7.

 

As a recursive definition, we would write it as:

   a₁ = 7

   a_n = 2*a_n-1      [for n>1]

 

     Using a recursive definition, you must find all of the previous terms before you could find the n^th term.

 

As an explicit definition, we would write it as:

   a_n = 7*2^n-1      [for n>0]

       Using an explicit definition, you may find a term directly.  For example, the 5^th term in this sequence, 

          a₅ = 7*2^5-1 = 7*2⁴ = 7*16 = 112