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Sagot :
Answer:
The explicit rule of the geometric sequence
aₙ = 187.5 (0.8)ⁿ⁻¹
Step-by-step explanation:
Step(i):-
Given that the third term of the sequence = 120
tₙ = a rⁿ⁻¹
t₃ = a r³⁻¹ = ar²
120 = ar² ..(i)
Given that the fifth term of the given geometric sequence = 76.8
tₙ = a rⁿ⁻¹
t₅ = a r⁵⁻¹ = a r⁴
76.8 = a r⁴...(ii)
Step(ii):-
Dividing (ii) and (i)
[tex]\frac{ar^{4} }{ar^{2} } = \frac{76.8}{120}[/tex]
r² = 0.64
r =√ 0.64 = 0.8
Substitute r= 0.8 in equation (i)
120 = ar²
120 = a(0.8)²
⇒ [tex]a = \frac{120}{0.64} =187.5[/tex]
Step(iii):-
The explicit rule of the geometric sequence
aₙ = a rⁿ⁻¹
put a= 187.5 and r = 0.8
aₙ = 187.5 (0.8)ⁿ⁻¹
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