Question

Given the sequence: 25, 21, 17, 13,... Write the explicit equation that models the sequence.

Answer 1

Answer:

The explicit equation that models the sequence is $f(n)=25-4(n-1)$.

Step-by-step explanation:

An arithmetic sequence is a list of numbers with a definite pattern. If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant then it is an arithmetic sequence.

The constant difference in all pairs of consecutive or successive numbers in a sequence is called the common difference.

In general, this is the standard explicit formula of an arithmetic sequence whose first term is A and common difference is B:

                                                 $f(n)=A+B(n-1)$

The sequence {25, 21, 17, 13, ...} is an example of an arithmetic sequence the same number, -4, is subtracted to each term to get to the next term.

We know the first term is 25 and common difference is -4.

Applying the standard explicit formula of an arithmetic sequence we get that

$f(n)=25-4(n-1)$.