Question

Write an explicit formula for the sequence -3, 1, 5, 9....

a. an = -3 + 4(n-1)

b. an = -3 + 4n

c. an = -3 + (n-1)

d. an = -3 + 4(n+1)

Answer 1

A. an = -3 + 4(n - 1)

Explanation:

The sequence given follows an arithmetic progression. This means the following term can be gotten by simply adding a factor to the previous term (or even the first term).

They are represented by the equation:

y(n) = a + r(n - 1)

Where y(n) is the nth term

a = first term

r = factor

Let us compare this with the sequence given:

The first term, a, is -3

We can get the factor, r, by using the second term, which is 1. This means n = 2.

=> 1 = -3 + r (2 - 1)

1 = -3 + r

=> r = 1 + 3 = 4

Therefore, putting a = -3 and r = 4, the sequence can be written as:

y(n) = -3 + 4(n - 1)