Answer:
a₁₇ = 196608
Step-by-step explanation:
The nth term of a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex]r^{n-1}[/tex]
where a₁ is the first term and r the common ratio
Given a₃ = 12 and a₅ = 48 , then
a₁ r² = 12 → (1)
a₁ [tex]r^{4}[/tex] = 48 → (2)
Divide (2) by (1)
[tex]\frac{a_{1}r^{4} }{a_{1}r^{2} }[/tex] = [tex]\frac{48}{12}[/tex] , that is
r² = 4 ( take square root of both sides )
r = 2
substitute r = 2 into (1)
a₁ 2² = 12
4a₁ = 12 ( divide both sides by 4 )
a₁ = 3
Then
a₁₇ = 3 × [tex]2^{16}[/tex] = 3 × 65336 = 196608
Answer:
a₁₇ = 196608
Step-by-step explanation:
The nth term of a geometric sequence is = a₁ where a₁ is the first term and r the common ratio.
Given a₃ = 12 and a₅ = 48 , then
a₁ r² = 12 → (1)
a₁ = 48 → (2)
Divide (2) by (1)
= , that is
r² = 4 ( take square root of both sides )
r = 2
substitute r = 2 into (1)
a₁ 2² = 12
4a₁ = 12 ( divide both sides by 4 )
a₁ = 3
Then
a₁₇ = 3 × = 3 × 65336 = 196608
Hence, the correct answer is a₁₇ = 196608
