Question

What is the rule for the sequence with the first four terms below?

Answer 1

Answer: f (x) = 0.75 minus 0.25x

Step-by-step explanation:

In an arithmetic sequence, the consecutive terms differ by a common difference.

The formula for determining the nth term of an arithmetic sequence is expressed as

an = a1 + (n - 1)d

Where

a1 represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

From the information given,

a1 = 0.5

d = 0.25 - 0.5 = - 0.25

n = 25

The rule for the sequence is

an = 0.5 + (n - 1)-0.25

an = 0.5 - 0.25n + 0.25

an = 0.5 + 0.25 - 0.25n

an = 0.75 - 0.25n

Substituting f(x) for an and x for n, it becomes

f(x) = 0.75 - 0.25x