Question

amdm.dsr.7.9 (mc)
what is the explicit equation for this sequence?
(8,12,16,20,24)
$a_n = 4 + 8(n - 1)$
$a_n = 8 - 4n$
$a_n = 0 + 4n$
$a_n = 8 + 4(n - 1)$

Explanation:

Step1: Identify sequence type

This is an arithmetic sequence, with first term $a_1=8$, common difference $d=12-8=4$.

Step2: Recall arithmetic explicit formula

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

Step3: Substitute values into formula

Substitute $a_1=8$ and $d=4$: $A_n = 8 + 4(n-1)$.

Step4: Verify with terms

For $n=2$: $A_2=8+4(2-1)=12$, which matches the sequence. For $n=3$: $A_3=8+4(3-1)=16$, which also matches.

Answer:

$A_n = 8 + 4(n - 1)$