If for G.P r= 1/3 and S_4=80/27 then a =
Answers
Answer:
80
Step-by-step explanation:
See the image for answer
For G.P r= 1/3 and S₄=80/27 value of a is 2
Given : A G.P.
r = 1/3
S₄ = 80/27
To Find : Value of a
Solution :
Geometric sequence
A sequence of numbers in which the ratio between consecutive terms is constant and called the common ratio.
a , ar , ar² , ... , arⁿ⁻¹
The nth term of a geometric sequence with the first term a and the common ratio r is given by: aₙ = arⁿ⁻¹
Sum is given by Sₙ = a(rⁿ - 1)/(r - 1)
Sum of infinite series is given by a/(1 - r) where -1 < r < 1
Geometric Series
The sum of the terms of a geometric sequence is called a geometric series.
a = ?
r = 1/3
n = 4
S₄ = 80/27
a((1/3)⁴⁻¹ )/(1/3 - 1) = 80/27
=> a (-80/81)/(-2/3) = 80/27
=> a = 2
Value of a is 2
GP is
2 , 2/3 , 2/9 , 2/27 , ...
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