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Thursday, July 22, 2010
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Team members:
- Imanina
- Shafiqah
- Hidayah
- Syazlina
- Shakirin
- Fathiah
- Fadhlina
- Faizatul Fazlin
- Eliani Hanis
- Azirah Alfaizah
- Asma'
- Fakhitah
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- Nurul Syuhada
Wednesday, July 21, 2010
Q13
That Tn is a geometric sequence.If the third term ,Tn=128 and the sixth term Tn=16, find the first term, the common ratio and the sum of the first ten terms.
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Q14
The sum of the first four terms of a geometric series with common ratio ¼ is 425/32
b) calculate the sum to infinity
S ∞ = a/1-r
= 10
1-1/4
= 13 1/3
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Q12
Given that m2+m+1, m2+2m+11,and m2+3m+28 form three consecutive terms of a geometric sequence.find m
m2+3m+28 = m2+2m+11
m2+2m+11 m2+m+1
(m2+3m+28)( m2+m+1)= (m2+2m+11)2
m4+m3+m2+3m3+3m2+3m+28m2+28m+28=m4+2m3+11m2+2m3+4m2+22m+11m2+22m+121
m4-m4+m3+3m2-2m3+m2+28m2-11m2-4m2-11m2+3m+28m-22m+28-121=0
6m2-13m-93=0
m=31/6
m=-3
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Geometric Progression Formula:
The geometric progression formula is given below.
The general form of a geometric progression (GP) is a, ar, ar2, ar3, ... with a ≠ 0 and C.R = r ≠ 0
1. The nth term of the G.P is tn = arn–1
2. Sum of the first n terms in a G.P. Sn = a|1-rn| / |1-r|
example:
Find the 5th term of the G.P 64, 16, 4...
Solution:
a = 64, r =16 /64= 1/ 4, n = 5
tn = a rn-1 , t5 = a r5-1 = a r4
t5 = 64(1/4)4 = 64/256 = 1/4
5th term of the given geometric progression is 1/4.
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What is Geometric Progression?
Geometric progression (also known as geometric sequence) is a sequence of numbers where the ratio of any two adjacent terms is constant. The constant ratio is called the common ratio,
Examples of GP:
3,6,12,24,... is a geometric progression withr=2 10,−5,2.5,−1.25,... is a geometric progression withr=−21
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Q15
The sum of the first three terms of a geometric series is 7/4 and the sum to infinity of the series is 2. Find the first terms and the common ratio of the series.
Solution:
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Q16
A geometric series has first term a and a common ratio r. If Sn is the sum of the first n terms of the geometric series, show that
solution:
solution:
Q17
The nth term , Tn, of a sequence is given by Tn = (2 / 3) n-1
b) which term of the sequence is 64 / 729 ?
solution:
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Q18
The sum of the first and second terms of a geometric series is 108 and the sum of the third and fourth terms is 12. Find the two possible values of the common ratio and the corresponding values of the first term.
solution:
solution:
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Q19
If Sn denotes the sum of first n terms of this sequence, shows that S3n : Sn = r ²ⁿ + rⁿ + 1. In a particular sequence of this type, the ratio S15 : S5 is 1057, find the common ratio.
Solution:
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Q20
The sum of the first n terms of a geometric sequence is 4-(2ⁿ⁺²)(3⁻²ⁿ). Find the second term and the common ratio of the sequence.
solution:
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