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Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

High School Mathematics - 2
3.7 Sum of Geometric Series - Using Formula

Sn = a1(1 - rn)/(1 - r) where r is the common ratio
Sn is the sum of the first n terms in a sequence
a1 is the first term in the sequence
r is the common ratio in the geometric sequence
n is the number of terms you are adding


Example:
Find the sum of the first 10 terms of the geometric series: 4, 8, 16, 32, 64, . . .
Solution: a1 = 4
r = 2
a10 = a1 x r9 = 4 . 29 = 2048
Therefore: S10 = 4(1-210)/(1 - 2) = 4 . 1023 = 4092

Example:
Find S6 for the sequence: 3 x 4n-1
we need to know a1, n, and r.
a1 = 3 x 41-1 = 3 x 40 = 3 x 1 = 3
a2 = 3 x 42-1 = 3 x 41 = 3 x 4 = 12
r = a2/a1 = 12/3 = 4 Since we are being asked to find S6, n is 6.
Formula:
Sn = a1(1 - rn)/(1 - r) = 3(1 - 46)/(1 - 4)= 4095

Directions: Find the sum of the geometic series. Also write at least 5 examples of your own.
Q 1: Find the sum of the first 7 terms of: 1 + x + x2+ x3+ ........
x6 - 1/1-x
x7 - 1/x-1
1 - x7/x-1

Q 2: Find the sum of the first 7 terms of 12 + 36 + 108 + 324 + . . .
29001
13116
14990

Q 3: Find the sum of the first 6 terms of the series: 2+6+18+54+162+........+13122
13456
23451
19682

Q 4: Find the sum of the first 10 terms of 5 + 10 + 20 + 40+ . . .
5115
4500
3000

Q 5: Find the sum of the series: 1 + 2 + 22+ 23+ 24........+ 29 is
1023
1234
1400

Q 6: Find the sum of the first 10 terms of: 4-2+1-1/2+......
2 115/158
3 87/128
2 85/128

Question 7: This question is available to subscribers only!

Question 8: This question is available to subscribers only!


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