Answer:
2,125,760
Step-by-step explanation:
The first term (a) is 8
The fourth term is 216
Hence the sum of the first 12 term can be calculated as follows
= 8-8(3)^12/1-3
= 8-24^12/-2
= 2,125,760
The sum of first 12 terms is 2,125,760
Sum of the first 12 term = 2,125,760
For geometric sequence,
aₙ = arⁿ⁻¹
where
a = first term
r = common ratio
n = number of terms
Therefore,
a = 8
a₄ = 216
let's find the common ratio
216 = 8 × r⁴⁻¹
216 = 8 × r³
r³ = 216 / 8
r³ = 27
r = [tex]\sqrt[3]{27}[/tex]
r = 3
Let's find sum of the first 12 terms.
Sₙ = a (rⁿ - 1) / r - 1
S₁₂ = 8(3¹² - 1) / 3 - 1
S₁₂ = 8(531440) / 2
S₁₂ = 4251520 / 2
S₁₂ = 2,125,760
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