Rewrite the product as a power:
1 answer:
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Answer:
see explanation
Step-by-step explanation:
The nth term of a geometric progression is
= a₁
where a₁ is the first term and r the common ratio
Given a₅ = 162 and a₈ = 4374 , then
a₁ = 162 → (1)
a₁ = 4374 → (2)
Divide (2) by (1)
=
r³ = 27
r = = 3
Substitute r = 3 into (1) and solve for a₁
a₁ = 162
81a₁ = 162
a₁ = = 2
Then
a₂ = a₁ × 3 = 2 × 3 = 6
a₃ = a₂ × 3 = 6 × 3 = 18
The first 3 terms are 2, 6, 18
(ii)
The sum to n terms of a geometric progression is
=
, then
=
=
= 59049 - 1
= 59048