Complete the recursive formula of the geometric sequence 56\,,-28\,,\,14\,,-7,...56,−28,14,−7,...56, comma, minus, 28, comma, 14, comma, minus, 7, comma, point, point, point. d(1)=d(1)=d, left parenthesis, 1, right parenthesis, equals d(n)=d(n-1)\cdotd(n)=d(n−1)⋅d, left parenthesis, n, right parenthesis, equals, d, left parenthesis, n, minus, 1, right parenthesis, dot

Answer:

Step-by-step explanation:

[tex]r=\frac{-28}{56}=-\frac{1}{2}\\a_{n}=\frac{-1}{2}a_{n-1}[/tex]

The recursive formula for the sequence is aₙ = (-1/2) * aₙ₋₁

A sequence of numbers such that the consecutive term is increasing or decreasing by a fixed ratio is called a geometric series.

The standard equation for geometric series is

Tₙ = a₁ rⁿ⁻¹

The formula above represents the explicit formula to determine the nth term of the sequence.

The recursive formula is used to determine the nth term when (n-1) th term is given.

The geometric sequence is,

56, -28, 14, -7,.................

The first term of the sequence is 56

The common ratio is determined by taking the ratio of the second term to the first term.

r = -28/56 = -1/2

The recursive formula is represented by,

aₙ = r * aₙ₋₁

aₙ = (-1/2) * aₙ₋₁

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