The value of x and y are 8 and 12 respectively.
The value of T₁₅ of the geometric progression is 1167.72
4, x, y, 18
4, x, y
The first three terms forms an arithmetic progression. Therefore,
AP formula
where
a = first term
d = common difference
n= number of term
Therefore,
3rd term
y = 4 +(3 - 1)(x-4)
y = 4 + 2(x - 4)
y = 4 + 2x - 8
y - 2x = -4
y = 2x - 4
x, y, 18
GP formula
where
a = first term
r = common ratio
Therefore,
a = x
r = 18 / y
18 = x(18 / y)²
18 = 324x / y²
18y² = 324x
x = 18y² / 324
x = y² / 18
Combine the equation
y = 2(y² / 18) - 4
y = y² / 9 - 4
y - y² / 9 = -4
9y - y²/9 = -4
-y² + 9y = -36
y² - 9y - 36 = 0
y² + 3y - 12y - 36 = 0
(y - 12)(y + 3)
y = 12 or - 3
x = 12² / 18 = 144 / 18 = 8
a₁₅ = ar¹⁵⁻¹
a₁₅ = 4 × (12 / 8)¹⁴
a₁₅ = 4 × (3 / 2)¹⁴
a₁₅ = 4 × 291.929260254
a₁₅ = 1167.71704102
a₁₅ = 1167.72
learn more on arithmetic and geometric progression here:https://brainly.com/question/21093837
