It's a geometric sequence
Test with third term to verify
Verified
Now
find formula
[tex]\\ \tt\hookrightarrow a_n=ar^{n-1}[/tex]
[tex]\\ \tt\hookrightarrow a_n=112(1/4)^{n-1}[/tex]
Answer:
[tex]a_n=112 \cdot \left(\dfrac14 \right)^{n-1}[/tex]
Step-by-step explanation:
The difference between each term in the sequence is not the same, therefore the sequence is a geometric sequence.
Geometric sequence formula: [tex]a_n=a r^{n-1}[/tex]
where [tex]a[/tex] is the start term and [tex]r[/tex] is the common ratio
Given [tex]a_1 = 112 \implies a=112[/tex]
To calculate [tex]r[/tex], divide one term by its previous term:
[tex]\implies r=\dfrac{a_3}{a_2}=\dfrac{7}{28}=\dfrac14[/tex]
Therefore, [tex]a_n=112 \cdot \left(\dfrac14 \right)^{n-1}[/tex]
