Question

Write an explicit formula for an, the nth term of the sequence 112, 28, 7, ....

Answer 1

Answer:

$a_n=112 \cdot \left(\dfrac14 \right)^{n-1}$

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:  $a_n=a r^{n-1}$

where $a$ is the start term and $r$ is the common ratio

Given $a_1 = 112 \implies a=112$

To calculate $r$, divide one term by its previous term:

$\implies r=\dfrac{a_3}{a_2}=\dfrac{7}{28}=\dfrac14$

Therefore, $a_n=112 \cdot \left(\dfrac14 \right)^{n-1}$

Answer 2

It's a geometric sequence

• r=112/28=1/4

Test with third term to verify

• 28(1/4)=7

Verified

Now

find formula

$\\ \tt\hookrightarrow a_n=ar^{n-1}$

$\\ \tt\hookrightarrow a_n=112(1/4)^{n-1}$