How do you tell whether the sequence with the terms $a_{3} = 21, a_{5} = 27, a_{12} = 48$ $a_3=21, a_5=27, a_12=48$ is arithmetic?

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How do you tell whether the sequence with the terms $a_{3} = 21, a_{5} = 27, a_{12} = 48$ $a_3=21, a_5=27, a_12=48$ is arithmetic?

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Answer 1 · 2017-03-09T10:02:25

It is an arithmetic series. See details below.

Explanation:

In an arithmetic series we can find common difference between two terms $a_{m}$ $a_m$ and $a_{n}$ $a_n$ by using formula $d = \frac{a_{n} - a_{m}}{n - m}$ $d=(a_n-a_m)/(n-m)$ , if common difference is same throughout, we can say this is an arithmetic sequence.

Here we can get three values of $d$ $d$

$\frac{a_{5} - a_{3}}{5 - 3} = \frac{27 - 21}{2} = \frac{6}{2} = 3$ $(a_5-a_3)/(5-3)=(27-21)/2=6/2=3$
$\frac{a_{12} - a_{5}}{12 - 5} = \frac{48 - 27}{7} = \frac{21}{7} = 3$ $(a_12-a_5)/(12-5)=(48-27)/7=21/7=3$ and
$\frac{a_{12} - a_{3}}{12 - 3} = \frac{48 - 21}{9} = \frac{27}{3} = 3$ $(a_12-a_3)/(12-3)=(48-21)/9=27/3=3$

As we get $d$ $d$ as constantly same, it is an arithmetic series.

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How do you tell whether the sequence with the terms $a_{3} = 21, a_{5} = 27, a_{12} = 48$ $a_3=21, a_5=27, a_12=48$ is arithmetic?

1 Answer

Explanation:

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How do you tell whether the sequence with the terms a_3=21, a_5=27, a_12=48a3=21,a5=27,a12=48a_3=21, a_5=27, a_12=48 is arithmetic?

1 Answer

Explanation:

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How do you tell whether the sequence with the terms $a_{3} = 21, a_{5} = 27, a_{12} = 48$ $a_3=21, a_5=27, a_12=48$ is arithmetic?