Question

please help asap
Instructions:Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each explicit formula to its corresponding recursive formula.

Answer 1

$1.f(n) = 4 + {5}^{n - 1} \\ 2.f(n) = 8 + 8(n - 1) \\ 3.f(n) = 8 + 3(n - 1)$

Answer 2

Given :  Different functions

To find : Equivalent functions

Solution:

f(n) = 3 + 8(n - 1)

=> f(1) = 3

but f(1) = 8  so not possible

f(n) = 4 + 5(4)ⁿ⁻¹

f(1) = 4 + 5(4)⁰ = 4 + 5 = 9

not possible

f(n) = 8 + 3(n - 1)

=> f(1) = 8

f(2) = 8 + 3  = 11

f(n) = 8 + 3(n - 1)

f(n + 1) = 8 +3n =  8 + 3(n - 1) + 3

=> f(n + 1) = f(n)+ 3

=> f(n) = f(n-1) + 3

f(n) = 8 + 3(n - 1)  =  f(n) = 3 + f(n-1)  

f(n) = 8 + 8(n-1) = 8n

=> f(1) = 8

f(n+1) = 8 + 8n

=> f(n+1) = 8 + f(n)

=> f(n) = 8 + f(n-1)

=> f(n) = 8 + 8(n-1) =  f(n) =   f(n-1) + 8

f(n) = 4 + 4(5)ⁿ⁻¹

f(1) = 4 + 4(5)⁰ = 4 + 4= 8

f(n + 1) =  4 + 4(5)ⁿ

= 4 + 4* 5 * (5)ⁿ⁻¹

= 4 + 4* 5 * (5)ⁿ⁻¹ + 16 - 16

= 20 +  4* 5 * (5)ⁿ⁻¹   - 16

= 5( 4 + 4(5)ⁿ⁻¹ ) - 16

= 5f(n) - 16

=> f(n) = 5f(n-1 ) - 16

f(n) = 4 + 4(5)ⁿ⁻¹ =  f(n) = 5f(n-1 ) - 16

f(n) = 5f(n-1 ) - 16  =  f(n) = 4 + 4(5)ⁿ⁻¹

f(n) =   f(n-1) + 8  = f(n) = 8 + 8(n-1)

f(n) = 3 + f(n-1)   = f(n) = 8 + 3(n - 1)

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