Answer:
the first term is 4
Step-by-step explanation:
Given
G(3) = 36
G(6) = 972
Solution:
General formula for geometric series
G(x) = AB^x
From given data: G(6)/G(3) = 972/36 = 27
From formula: G(6)/G(3) = AB^6/(AB^3) = B^3
Therefore
B^3 = 27
B=3
Hence
G(1) = AB^1 = AB^3/B^2=36/3^2=36/9=4
Ans: the first term is 4
Answer:
a₁ = 4
Step-by-step explanation:
The n th term of a geometric series is
[tex]a_{n}[/tex] = a₁ [tex]r^{n-1}[/tex]
where a₁ is the first term and r the common ratio
Given a₃ = 36 and a₆ = 972 , then
ar² = 36 → (1)
a[tex]r^{5}[/tex] = 972 → (2)
Divide (2) by (1)
[tex]\frac{ar^{5} }{ar^{2} }[/tex] = [tex]\frac{972}{36}[/tex] , that is
r³ = 27 ( take the cube root of both sides )
r = [tex]\sqrt[3]{27}[/tex] = 3
Substitute r = 3 into (1)
9a = 36 ( divide both sides by 9 )
a = 4
The first term is 4
