F(n+1)=f(n)-5. If f(1)=100, what is f(6)

Mathematics

1 answer:

PilotLPTM [1.2K]3 years ago

8 0

Answer:

Step-by-step explanation:

Given:

f(1) = 100

f(n+1) = f(n) - 5

Solve for:

f(6)

Solution:

f(1) = 100

f(2) = f(1) - 5 = 100 - 5 = 100 - 1 x 5 = f(1) - 1 x 5

f(3) = f(2) - 5 = 100 - 5 - 5 = 100 - 2 x 5 = f(1) - 2 x 5

...

f(n) = f(n - 1) - 5 = 100 - (n-1) x 5 = f(1) - (n-1) x 5

=> f(6) = f(1) - (6-1) x 5 = 100 - 5 x 5 = 100 - 25 = 75

Hope this helps!

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A shopkeeper allows 15% discount on the marked price, still he manages to have 7% profit. How much high did he mark his goods ab

lianna [129]

Answer: $25.9\%$

Step-by-step explanation:

Given

Shopkeeper allows 15% discount on the marked price and still manages a profit of 7%

Suppose the marked price is $x$

So, the selling price is $(1-0.15)x=0.85x$

Suppose the cost price is $y$

$\Rightarrow \dfrac{0.85x-y}{y}=7\%\\\\\Rightarrow \dfrac{0.85x}{y}-1=0.07\\\\\Rightarrow \dfrac{0.85x}{y}=1.07\\\\\Rightarrow y=\dfrac{0.85x}{1.07}\\\\\Rightarrow y=0.794x$

So, the percentage the shopkeeper marked his goods above cost price

$\Rightarrow \dfrac{x-y}{y}\times 100\\\\\Rightarrow \dfrac{x-0.794x}{0.794}\times 100\\\\\Rightarrow \dfrac{0.2056}{0.794x}\times 100\\\\\Rightarrow 25.89\%\approx 25.9\%$