Question

Carlos and ana were asked to find an explicit formula for the sequence -10, -4, 2, 8, ..., where the first term should be f(1).

Carlos said the formula is f(n)= -10 + 6n
Ana said the formula is f(n)= -10 + 6(n-1)

Which one of them is right?
a) only carlos
b) only ana
c) both carlos and ana
d) neither carlos nor ana

Answer 1

Carlos is right and the formula for the sequence is f(n) = -10 + 6n.Option A is the correct answer.Carlos is correct with f(n) = -10 + 6n, producing the correct sequence terms. Ana's formula is incorrect.

Step-by-step explanation:

Carlos and Ana were asked to find an explicit formula for the sequence -10, -4, 2, 8, ..., where the first term should be f(1). Carlos said the formula is f(n)= -10 + 6n and Ana said the formula is f(n)= -10 + 6(n-1). To determine who is correct, we can substitute the given values of n into both formulas and check if they produce the correct terms of the sequence. Let's check:

For n = 1, Carlos' formula gives f(1) = -10 + 6(1) = -4, which is the first term in the sequence. Ana's formula gives f(1) = -10 + 6(1-1) = -10, which is not correct.

Therefore, Carlos is right and the formula for the sequence is f(n) = -10 + 6n.