Answer:
a) [tex]t_{1} = 12[/tex]
b) The explicit formula
[tex]t_{n} = ar^{n-1} = 12(2.5)^{n-1}[/tex]
c) t₁₈ = 69,849,193.096
Step-by-step explanation:
Step(i):-
Given that the geometric sequence
r = 2.5
Given the fourth term of the geometric sequence
[tex]t_{4} = ar^{3} = 187.5[/tex]
⇒ ar³ = 187.5
⇒ a (2.5)³ = 187.5
[tex]a = \frac{187.5}{(2.5)^{3} } = 12[/tex]
The explicit formula
[tex]t_{n} = ar^{n-1} = 12(2.5)^{n-1}[/tex]
Step(ii):-
put n=1
[tex]t_{1} = ar^{1-1} = 12(2.5)^{1-1} = 12 (2.5)^{0} = 12[/tex]
The [tex]18^{th}[/tex] of the geometric sequence
[tex]t_{18} = ar^{18-1} = a r^{17}[/tex]
[tex]t_{18} = 12( 2.5)^{17}[/tex]
t₁₈ = 69,849,193.096
Final answer:-
a) [tex]t_{1} = 12[/tex]
b) The explicit formula
[tex]t_{n} = ar^{n-1} = 12(2.5)^{n-1}[/tex]
c) t₁₈ = 69,849,193.096
