The given geometric sequence, with first term = 4 and ratio = 0.1, has the formula for its nth term: a(n) = 4 . 0.1ⁿ⁻¹. The first five terms are: 4, 0.4, 0.04, 0.004, 0.0004
The formula of the nth term of a geometric sequence is:
a(n) = a₁ . r^(n-1)
with a₁ is the first term and r is the ratio. In a geometric sequence, the ratio is constant and equal to a(n)/a(n-1).
In the given problem, a₁ =4, r=0.1, therefore:
a(n) = a₁ . r^(n-1)
a(n) = 4 . 0.1ⁿ⁻¹
To find the first five terms, replace n with 1, 2, 3, 4, and 5.
a₁ = 4
a(2) = 4 . 0.1²⁻¹
= 4 . 0.1¹ = 0.4
a(3) = 4 . 0.1³⁻¹
= 4 . 0.1² = 0.04
a(4) = 4 . 0.1⁴⁻¹
= 4 . 0.1³ = 0.004
a(5) = 4 . 0.1⁵⁻¹
= 4 . 0.1⁴ = 0.0004
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