Answer:
a₄ = 1029
a₅ = 7203
Step-by-step explanation:
a₁ = 3
aₙ = aₙ₋₁ x 7
ₐ₂ = a₂₋₁ x 7 = a₁ x 7 = 3 x 7 = 21
a₃ = 21 x 7 = 147
a₄ = 147 x 7 = 1029
a₅ = 1029 x 7 = 7203
The geometrical sequence terms [tex]a_{4} = 1029[/tex] and [tex]a_{5} = 7203[/tex]
"A geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio."
We have
Geometric sequence terms
[tex]a_{1}[/tex] = 3
[tex]a_{n} = a_{n-1}[/tex] × [tex]7[/tex]
We have to find the [tex]a_{4}[/tex], [tex]a_{5}[/tex]
First we have to find geometric sequence terms [tex]a_{2}[/tex] and [tex]a_{3}[/tex]
[tex]a_{2} = a_{2-1}[/tex] × 7
⇒ [tex]a_{2} = a_{1}[/tex] × [tex]7[/tex]
⇒ [tex]a_{2} = 3[/tex] × [tex]7[/tex]
⇒ [tex]a_{2} = 21[/tex]
[tex]a_{3} = a_{3-1}[/tex] × [tex]7[/tex]
⇒ [tex]a_{3} = a_{2}[/tex] × [tex]7[/tex]
⇒ [tex]a_{3} = 21[/tex] × [tex]7[/tex]
⇒ [tex]a_{3}= 147[/tex]
[tex]a_{4} = a_{4-1}[/tex] × 7
⇒ [tex]a_{4} = a_{3}[/tex] × [tex]7[/tex]
⇒[tex]a_{4} = 147[/tex] × [tex]7[/tex]
⇒ [tex]a_{4} = 1029[/tex]
[tex]a_{5} = a_{5-1}[/tex] × [tex]7[/tex]
⇒ [tex]a_{5} = a_{4}[/tex] × [tex]7[/tex]
⇒ [tex]a_{5} = 1029[/tex] × [tex]7[/tex]
⇒ [tex]a_{5} = 7203[/tex]
Hence, geometric sequence terms [tex]a_{4} = 1029[/tex] and [tex]a_{5} = 7203[/tex]
Lear more about geometrical sequence here
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