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General Form of an AP

Find the comm...

Question

Find the common difference $d$ for an AP, where $a_{1} = 10$ and $a_{20} = 466$

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Solution

In a arithmetic series $a_{n} = a + (n - 1) d$ where $a$ is the first term of the sequence, $d$ is the common difference, and $n$ is the number of the term to find.

Since the first term is $10$ , therefore,

$a_{20} = 10 + (20 - 1) d = 10 + 19 d$
$466 = 10 + 19 d$
$466 - 10 = 19 d$
$19 d = 456$
$d = 24$

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