Question

Select the correct answer.
What is the sum of the first eight terms of a geometric series whose first term is 3 and whose common ratio is 1/2?

A. 3/128
B. 255/128
C. 765/128
D. 255/256

Answer 1

The answer is Going to be C

Answer 2

Answer:  (C) = 765/128

Step-by-step explanation:

Formula for finding the sum of a geometric series is in two form namely

i)   Sn =  a(1 - r[^{n})

              -------------    when r ∠ 1    

                 1 - r

ii)   Sn =   a( r ^{n} - 1 )

                ---------------  when r greater than 1

                    r - 1  

From the question, a = 3, n = 8 and r = 1/2 or o.5

from the formula i and ii above

i will be applicable because r ∠ 1

S8 = 3( 1 - 1/2^{8])

          ----------------

               1 - 1/2

      =  3 ( 1 - 1/256)

              -----------------

                     1/2

     =  3( 256 -1 /256)

           -------------

                 1/2

     =   3(255/256)

          ----------------

                 1/2

   =   3 x 255 x 2

        ----------------

            256

    =   765/128