Question

question 13
4 pts
amdm.dsr.7.9 (mc)
what is the explicit equation for this sequence?
(9, 5, 1, -3, -7)
aₙ = 13 - 2n
aₙ = 13 + 4n
aₙ = 0 - 4n
aₙ = 13 - 4n

Explanation:

Step1: Identify sequence type

This is an arithmetic sequence, with first term $a_1=9$, common difference $d=5-9=-4$.

Step2: Recall arithmetic explicit formula

The explicit formula for an arithmetic sequence is $A_n = a_1 + (n-1)d$.

Step3: Substitute values into formula

$$\begin{align*} A_n &= 9 + (n-1)(-4)\\ &= 9 -4n +4\\ &= 13 -4n \end{align*}$$

Step4: Verify with terms

For $n=1$: $13-4(1)=9$, $n=2$: $13-4(2)=5$, which matches the sequence.

Answer:

D. $A_n = 13 - 4n$