Question

A sequence is defined by aₙ=n² for n≥1. Diego writes an equation for the n-th term of the sequence as aₙ=2n. Is he correct?

a) Yes, the equations are equivalent.
b) No, the equations are not equivalent.
c) Yes, but only for even values of n.
d) No, and the correct equation is aₙ=n².

Answer 1

Diego's equation, aₙ = 2n, is not equivalent to the sequence defined by aₙ = n². The correct equation for the n-th term of the sequence is aₙ = n². The correct answer is option b).

Step-by-step explanation:

To determine if Diego's equation, aₙ = 2n, is equivalent to the sequence defined by aₙ = n², we can compare the terms of both equations. For the sequence aₙ = n², the first few terms are: a₁ = 1, a₂ = 4, a₃ = 9, a₄ = 16, ... For the equation aₙ = 2n, the terms are: a₁ = 2, a₂ = 4, a₃ = 6, a₄ = 8, ...

By comparing the terms, we can see that the two equations are not equivalent. In the sequence defined by aₙ = n², the terms increase as the square of the term number, while in the equation aₙ = 2n, the terms increase linearly. Therefore, the correct equation for the n-th term of the sequence is aₙ = n².