The first terms and explicit formulas for the given geometric sequences are:
a₁ = 1.7, Explicit formula: aₙ = 1.7 *6ⁿ⁻¹
a₁ = 3, Explicit formula: aₙ = 3 * (-3)ⁿ⁻¹
a₁ = 3.1, Explicit formula: aₙ = 3.1 * 5ⁿ⁻¹
a₁ = 5, Explicit formula: aₙ = 5* 4ⁿ⁻¹
What is geometric sequence?
Given
the first term a₁
The explicit formula for a geometric sequence is given by:
aₙ = a₁ * rⁿ⁻¹
where:
aₙ is the nth term,
a₁ is the first term,
r is the common ratio, and
n is the term number.
Let's find a₁ and the explicit formula for each case:
For a₁ = 1.7 and r = 6.0
a₁ = 1.7
Explicit formula: aₙ = 1.7 *6ⁿ⁻¹
For a₁ = 3 and r = -3
a₁ = 3
Explicit formula: aₙ = 3 * (-3)ⁿ⁻¹
For a₁ = 3.1 and r = 5.0
a₁ = 3.1
Explicit formula: aₙ = 3.1 * 5ⁿ⁻¹
For a₁ = 5 and r = 4
a₁ = 5
Explicit formula: aₙ = 5* 4ⁿ⁻¹