The sequence and their functions are:
- f(n) = f(n - 1) + 7 ⇒ 3, 10, 17, 24, 31.....
- f(n) = f(n - 1) + 4n - 2 ⇒ 3, 9, 19, 33, 51.....
- f(n) = 2[f(n - 1)] ⇒ 3, 6, 12, 24, 48.....
<h3>How to match the functions?</h3>
To do this, we simply set values for n and calculate the function values using the current value of n.
So, we have:
<u>Function 1: f(n) = f(n - 1) + 6n - 5 where f(1) = 3</u>
Let n = 2
f(2) = f(1) + 6(2) - 5 = 3 + 12 - 5 = 10
Let n = 3
f(3) = f(2) + 6(3) - 5 = 10 + 18 - 5 = 23
None of the sequence follows the pattern 3, 10, 23....
<u>Function 2: f(n) = f(n - 1) + 2n - 1 where f(1) = 3</u>
Let n = 2
f(2) = f(1) + 2(2) - 1 = 3 + 4 - 1 = 6
Let n = 3
f(3) = f(2) + 2(3) - 1 = 6 + 6 - 1 = 11
None of the sequence follows the pattern 3, 6, 11....
<u>Function 3: f(n) = f(n - 1) + 6 where f(1) = 3</u>
Let n = 2
f(2) = f(1) + 6 = 3 + 6 = 9
Let n = 3
f(3) = f(2) + 6 = 9 + 6 = 15
None of the sequence follows the pattern 3, 9, 15....
<u>Function 4: f(n) = f(n - 1) + 7 where f(1) = 3</u>
Let n = 2
f(2) = f(1) + 7 = 3 + 7 = 10
Let n = 3, 4 and 5
f(3) = f(2) + 7 = 10 + 7 = 17
f(4) = f(3) + 7 = 17 + 7 = 24
f(5) = f(4) + 7 = 24 + 7 = 31
So, we have:
f(n) = f(n - 1) + 7 ⇒ 3, 10, 17, 24, 31.....
<u>Function 5: f(n) = f(n - 1) + 4n - 2 where f(1) = 3</u>
Let n = 2
f(2) = f(1) + 4(2) - 2 = 3 + 8 - 2 = 9
Let n = 3, 4 and 5
f(3) = f(2) + 4(3) - 2 = 9 + 12 - 2 = 19
f(4) = f(3) + 4(4) - 2 = 19 + 16 - 2 = 33
f(5) = f(4) + 4(5) - 2 = 33 + 20 - 2 = 51
So, we have:
f(n) = f(n - 1) + 4n - 2 ⇒ 3, 9, 19, 33, 51.....
<u>Function 6: f(n) = 2[f(n - 1)] where f(1) = 3</u>
Let n = 2
f(2) = 2 * f(1) = 2 * 3 = 6
Let n = 3, 4 and 5
f(3) = 2 * f(2) = 2 * 6 = 12
f(4) = 2 * f(3) = 2 * 12 = 24
f(5) = 2 * f(4) = 2 * 24 = 48
So, we have:
f(n) = 2[f(n - 1)] ⇒ 3, 6, 12, 24, 48.....
Read more about sequence at:
brainly.com/question/6561461
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