Determine the the fourth
the geometric sequence. x; 2x+2; 3x+3.
numerical
value
Of
term
OF

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 × = -

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step-by-step explanation:

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