given the sequence: 25, 21, 17, 13,... write the explicit equation that models the sequence. (hint: simplify…

given the sequence: 25, 21, 17, 13,... write the explicit equation that models the sequence. (hint: simplify your equation.)

given the sequence: 25, 21, 17, 13,... write the explicit equation that models the sequence. (hint: simplify your equation.)

Answer

Explanation:

Step1: Identify the type of sequence

This is an arithmetic sequence. The first term (a_1 = 25). The common difference (d=21 - 25=- 4) (since (a_{n + 1}-a_{n}) gives (d), e.g., (21-25=-4), (17 - 21=-4), (13-17=-4)).

Step2: Use the formula for the (n)th term of an arithmetic sequence

The formula for the (n)th term of an arithmetic sequence is (a_{n}=a_{1}+(n - 1)d). Substitute (a_{1}=25) and (d=-4) into the formula: [ \begin{align*} a_{n}&=25+(n - 1)(-4)\ &=25-4n + 4\ &=29-4n \end{align*} ]

Answer:

(a_{n}=29 - 4n)