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const2013 [10]
2 years ago
12

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

Mathematics
2 answers:
enot [183]2 years ago
8 0

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}

mr Goodwill [35]2 years ago
6 0

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}

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