Question

Which one of the formulas below describes the sequence 2, 8, 14?

A) f(n) = 6n - 2
B) f(n) = 4n + 2
C) f(n) = 6n + 2
D) f(n) = 4n - 2

Answer 1

The sequence 2, 8, 14 is best described by the formula C) f(n) = 6n + 2, as it matches the given sequence when n takes on the values 0, 1, and 2 respectively.

Step-by-step explanation:

To find which formula describes the sequence 2, 8, 14, we can test each option by plugging in values of n sequentially starting from n = 1.

• f(n) = 6n - 2: For n=1, f(1) = 6*1 - 2 = 4 (does not match 2), for n=2, f(2) = 6*2 - 2 = 10 (does not match 8), so this is not the correct formula.
• f(n) = 4n + 2: For n=1, f(1) = 4*1 + 2 = 6 (does not match 2), for n=2, f(2) = 4*2 + 2 = 10 (does not match 8), so this is not the correct formula.
• f(n) = 6n + 2: For n=1, f(1) = 6*1 + 2 = 8, for n=2, f(2) = 6*2 + 2 = 14, and for n=0, f(0) = 6*0 + 2 = 2. This matches the sequence exactly, making it the correct formula.
• f(n) = 4n - 2: For n=1, f(1) = 4*1 - 2 = 2 (matches 2), for n=2, f(2) = 4*2 - 2 = 6 (does not match 8), so this is not the correct formula.

Therefore, the correct formula is C) f(n) = 6n + 2.