find the sum f the first 5 terms of the geometric sequence 1/2,2/3,8/9......
Answers
Answer:
4.819
Step-by-step explanation:
What is the sum of the first five terms in the geometric sequence 1/2, 2/3, 8/9…?
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The series is given 1/2, 2/3, 8/9.................
The first term a = 1/2 and
The common ratio r = ratio of second and first term = (2/3)/(1/2) = 4/3
The sum of n GP terms can be given by
Sn = a(r^n -1)/( r - 1)= 1/2[(4/3)∞- 1]/(4/3-1) = ∞ as n -> ∞
when n=5 Sn = 1/2(4/3^5 -1)/(4/3 -1) = 1/2(4.213 -1)/(1/3)
= 3.213*3 /2 = 9.639/2 = 4.819
Given : Geometric sequence 1/2,2/3,8/9....
To Find : Sum of first 5 terms
Solution:
Geometric sequence
a , ar , ar² , ...
a = first term
r = common ratio
1/2,2/3,8/9...
a = 1/2
r = (2/3)/(1/2) = 4/3
(8/9)/(2/3) = 4/3
Sₙ = a(rⁿ - 1)/(r - 1)
S₅ = (1/2)( (4/3)⁵ - 1) /(4/3 - 1)
= (3/2 )(1024/243 - 1)
= (3/2) ( 781 / 243)
= 781 / 162
Sum of first 5 terms is 781 / 162
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