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MTH100 GDB Solution & Discussion Last Date:13-12-2016

Question:

Find the sum of the geometric series   to 7th term by using formula for finding sum of geometric series.

Note:

If you successfully able to find the common ratio, then 25% marks will be awarded.

If you will write the correct formula for finding sum, then you will be awarded 50% marks.

Inserting correct values in formula, will give you 75% marks.

Find the correct sum will give you 100% marks.

Instructions:

  • The purpose of this GDB is to assess your knowledge and computational skills.
  • Produce you own work. Copying the text from any other student or from any website is strictly prohibited. You will get zero marks in this case.
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  • Last date of this GDB is Dec 13, 2016. There will not any relaxation after due date. You have ample days to complete this task. Submit your answers at the earliest to avoid losing your marks.

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commo

Series will be 1-2+4-8+16-32+64
Sum will be 43.

common ratio is -1/2

required in GDB 

1...common ratio 
2...using formula 
3...and answer of  sum  is 


series 
7 numbers of series will be                     
a1,a2,a3,a4,a5,a6,a7
1-2+4-8+16-32+64

Sum of 7 numbers =  43

r means the value that is multiplied with old number to make a new number 

like        1st number  = 1 * -2   =-2 (2nd number)
             2nd numebr = -2  * -2   =4 (3rd number 
              3rd number  = 4 * -2  = -8 (4th number )
i mean to say that 2 is the value that is producing new series number so r= -2 

a7= a1(r)^n-1 
a7= 1 (-2)^7-1
a7 = 2^6
a7 = 64 

to find 6th value using formula , apply this formula again 

common ratio sab mai same hotii hai  as proved below 
common ratio = -2 (if i m nt wrng)

example  = 
common ratio =  a2/a1   = -2/1   = -2 
                     =  a3/a2   = 4/-2   = -2 
                     = a4/a3    = -8/4   = -2 

From the question:

            a1 = 1

            a2 = -2

            a3 = 4

            n = 7

            Now

            Common ratio = r

            r = a2/a1 = a3/a2

            r = -2/1 = 4/-2 =-2

            r = -2

            Now sum = Sn

            Sn = a1 (1-r^n) / 1-r

            S7 = 1(1-(1-(-2^7)) / 1-(-2)

            S7 = 1+128 / 1+2

            S7 = 129 / 3

            S7 = 43

MTH100 GDB Solution 

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