The formula of the given geometric sequence is: a(n) = 1024 . (0.5)ⁿ⁻¹ and the first five terms are: 1024, 512, 256, 128, and 64.
The formula of the n-th term of a geometric sequence is:
a(n) = a₁ . r^(n-1)
Where:
a₁ is the first term
r is the ratio = a(n)/a(n-1)
Parameters given in the problem:
a₁ =1024, r=0.5
Plug these parameters into the formula, then we get the explicit formula of the n-th term:
a(n) = 1024 . (0.5)ⁿ⁻¹
The first 5 terms:
a₁ = 1024
a(2) = 1024 . (0.5)²⁻¹
= 1024 . (0.5)¹ = 512
a(3) = 1024 . (0.5)³⁻¹
= 1024 . (0.5)² = 256
a(4) = 1024 . (0.5)⁴⁻¹
= 11024 . (0.5)³ = 128
a(5) = 1024 . (0.5)⁵⁻¹
= 1024 . (0.5)⁴ = 64
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