Given a₁ = 100, r=-20, the explicit formula of the geometric sequence is: a(n) = 100 . (-20)ⁿ⁻¹, and the first five terms are: 100, -2000, 40000, -800000, 16000000
Let
a₁ = the first term
r = ratio
The n-th term of a geometric sequence is given by:
a(n) = a₁ . r^(n-1)
To find the explicit formula, substitute a₁ = 100, r=-20
a(n) = 100 . (-20)ⁿ⁻¹
The first 5 terms:
a₁ = 100
a(2) = 100 . (-20)²⁻¹
= 100 . (-20)¹ = -2,000
a(3) = 100 . (-20)³⁻¹
= 100 . (-20)² = 40,000
a(4) = 100 . (-20)⁴⁻¹
= 100 . (-20)³ = -800,000
a(5) = 100 . (-20)⁵⁻¹
= 100 . (-20)⁴ = 16,000,000
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