Question

Please I need this by Monday

Answer 1

(a) u₃ = 71.8768 (b) u₁ = 0.6

Explanation:

given the recursive formula

`u_(n+1)` = 2
`u_(n)`² - 7

this allows any term in the sequence to be found by multiplying the square of the previous term by 2 ,then subtracting 7

(a)

u₃ = 2u₂² - 7 ← substitute u₂ = - 6.28

u₃ = 2(- 6.28)² - 7

= 2(39.4384) - 7

= 78.8768 - 7

= 71.8768

(b)

from the formula , we can obtain

u₂ = 2u₁² - 7 ← substitute u₂ = - 6.28 and solve for u₁

- 6.28 = 2u₁² - 7 ( add 7 to both sides )

0.72 = 2u₁² ( divide both sides by 2 )

0.36 = u₁² ( take square root of both sides )

`√(0.36)` =
`\sqrt{u_(1)^2 }` , that is the positive value of u₁ is

0.6 = u₁