Question

What is the explicit equation for the nth term of the arithmetic sequence 6, 3.5, 1, –1.5, –4, …? an = 6 + 2.5n an = 6 – 2.5n an = 6 + 2.5(n + 1) an = 6 – 2.5(n – 1)

Answer 1

`a_n=6-2.5(n-1)`

Step-by-step explanation:

The arithmetic sequence formula is generally given as;

`\begin{gathered} a_n=a_1+(n-1)d \\ \text{where } \\ a_n=the\text{ nth term} \\ a_1=\text{ the first term} \\ n=term\text{ position} \\ d=\text{common difference} \end{gathered}`

From the given sequence, we can see that;

`\begin{gathered} a_1=6 \\ d=3.5-6=-2.5 \end{gathered}`

Let's now substitute the above values into the AP formula;

`\begin{gathered} a_n=6+(n-1)(-2.5) \\ a_n=6-2.5(n-1) \end{gathered}`