Construct an explicit rule from the sequence in the table.

Question

This is supposed to be a table but I don't know how to add it here.

Tickets 1 2 3 4

Total Cost ($) 12 22 32 42

Write an explicit rule from the sequence in the table above.

Multiple choice:

a. f(n) = 10n + 2

b. f(n) = 10n + 3

c. f(n) = 2n + 10

d. f(n) = 3n + 10

Answer 1

Since you have a multiple choice question, it would be fine to see which function fits the data in the table.

n = Input = tickets: 1 2 3 4

f(n) = Output = price $: 12 22 32 42

Choice a: f(n) = 10n + 2

f(1) = 10•1+2 = 12 √

f(2) = 10•2 +2 = 22 √

f(3) = 10•3+2 = 32 √

f(4) = 10•4+2 = 42 √

Since choice a gives the corresponding output for the input, for all inputs, it is the answer.

I will show the other answer choices fail.

Choice b: f(n) = 10n + 3

f(1) = 10•1+3 = 13 X

The output should be 12 when the input is 1.

Choice c: f(n) = 2n+10

f(1) = 2•1+10 = 12 √

f(2) = 2•2+10 = 14 X

The output should be 22 when the input is 2.

Choice d: f(n) = 3n+10

f(1) = 3•1+10 = 13 X

The output should be 12 when the input is 1.

Choice A, f(n) = 10n+2, is the correct answer.

Answer 2

Since there are so few values, the easiest way to do this is probably just testing each answer. Only one f(n) can be correct for all n tickets. Clearly, 10n + 2 is the only answer that fits all values of the table.

More generally, try to find a pattern as n changes. In this case, f(n+1) =f(n) + 10 as for every ticket, the price increases by $10. We can insert n = 0 here to get the base case. f(0+1) = f(0) + 10, and we know from the table f(1) = 12 so 12 = f(0) + 10 therefore f(0) = 2 and we have our equation f(n) = 10n +2.