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A sequence is defined by f(0) = -20, f(n) = f(n-1) - 5 forn > 1.

1. Explain why f(1) = -20 – 5.
2. Explain why f(3) = -20 – 5 – 5 – 5.
3. Complete the expression: f(10) = -20 –
. Explain your reasoning.

1 Answer

3 votes

Answer:

1. Proved down

2. proved down

3. f(10) = -20 - 5 - 5 - 5 - 5 - 5 - 5 - 5 - 5 - 5 - 5

Explanation:

Let us explain how to solve the question

∵ f(0) = -20, f(n) = f(n - 1) - 5 for n > 1

→ That means we have an arithmetic sequence with constant

difference -5 and first term -20

1. → f(1) means we need to find the second term, which equal the

term - 5

∵ f(1) means n = 1

∴ f(1) = f(1 - 1) - 5

∴ f(1) = f(0) - 5

∵ f(0) = -20

f(1) = -20 - 5 → Proved

2. → f(3) means we need to find the third term, which equal the

second term - 5

∵ f(3) means n = 3

∴ f(3) = f(3 - 1) - 5

∴ f(3) = f(2) - 5

→ f(2) = f(1) - 5

∵ f(1) = -20 - 5

∴ f(2) = [-20 - 5] - 5 = -20 - 5 - 5

∴ f(3) = [-20 - 5 - 5] - 5

f(3) = -20 - 5 - 5 - 5 → Proved

3. → From 1 and 2 we notice that the number of -5 is equal to n,

at n = 1 there is one (-5), when n= 3 there are three (-5)

∵ n = 10

∴ There are ten (-5)

∴ f(10) = -20 - 5(10)

f(10) = -20 - 5 - 5 - 5 - 5 - 5 - 5 - 5 - 5 - 5 - 5 → Proved

User Syakur Rahman
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