find the sum of the first five terms. 3, 12, 48.

Question

What is the geometric sequence

Answer 1

Each term is 4 times greater than the previous term; that is, a_n+1/a_n = 4.  The sequence is a_n = 3*4^(n-1), n=1, 2, 3, ...

 

n        a_n = 3*4^(n-1)

1              3                 3*4⁰

2            12                 3*4¹

3            48                 3*4²

4          192                 3*4³

5          768                 3*4⁴

           ------

sum = 1023

Answer 2

The pattern in this geometric sequence is "multiply by 4."  You can see this because each term multiplied by 4 gives the next term:  3 x 4 = 12; 12 x 4 = 48; etc.

 

Three terms are already given.  You need the first five terms to answer the question, so find terms 4 and 5 by following the pattern.

1st term = 3   (given in the question)

2nd term = 12   (given)

3rd term = 48   (given)

4th term = 48 x 4 = 192

5th term = 192 x 4 = 768

 

The question asks for the sum of the first five terms, so the answer is:

3 + 12 + 48 + 192 + 768  =  1,023

Answer 3

Formula for the sum of a finite geometric series is:  S_n = a₁(1 - rⁿ)

                                                                                    1 - r

 

a_{1 (first term)} = 3,

r (common ratio) = 4,

n = 5 (number of terms)           S₅ = 3(1 - 4⁵) = 3(1 - 1024) = 3(-1023)= -3069

                                                       1 - 4               -3              -3            -3

 

                                               S₅ = 1023

 

Or, you can just find the first five terms and add them together.

3, 12, 48, 192, 768      You are multiplying each term by 4 to find the next term.