Question

Which of the following equations could you use to find the nth term of a constant velocity sequence?

a) ( aₙ = a₁ + (n-1)d )

b) ( aₙ = a₁ × r(n-1) )

c) ( aₙ = a₁ + nr )

d) ( aₙ = a₁ ÷ (n-1) )

Answer 1

To find the nth term of a constant velocity sequence, the correct formula to use is aₙ = a₁ + (n-1)d, representing an arithmetic sequence where 'd' is the constant velocity.

Step-by-step explanation:

To find the nth term of a constant velocity sequence, we would want an equation that defines a sequence which increments by a constant amount each time. A constant velocity sequence is essentially an arithmetic sequence, because the distance covered between each consecutive term is the same, much like how arithmetic sequences have a common difference. Thus, the correct formula to use is an = a1 + (n-1)d, where an is the nth term, a1 is the first term, n is the term number, and d is the common difference (constant velocity in this context).

Let's go through each option:

• (a) an = a1 + (n-1)d correctly represents an arithmetic sequence, which is what a constant velocity sequence would be mathematically equivalent to.
• (b) an = a1 × r(n-1) is the formula for a geometric sequence, not appropriate for constant velocity.
• (c) an = a1 + nr assumes the velocity increases by nr each time, which is not constant.
• (d) an = a1 ÷ (n-1) suggests division per term which isn't relevant to constant velocity or arithmetic sequences.