Answer:
a₄ = -
Step-by-step explanation:
In a geometric sequence, the common ratio r is calculated as
r = =
, substitute values
=
( cross- multiply )
(2x + 2)² = x(3x + 3) ← expand both sides
4x² + 8x + 4 = 3x² + 3x ( subtract 3x² + 3x from both sides )
x² + 5x + 4 = 0 ← in standard form
(x + 1)(x + 4) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = - 1
x + 4 = 0 ⇒ x = - 4
However x ≠ - 1 as this would make the denominator of the second term equal to zero and therefore undefined.
Thus x = - 4 and
r = =
=
=
Then
a₁ = - 4
a₂ = - 4 × = - 6
a₃ = - 6 × = - 9
a₄ = - 9 × = -