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