How do I find the $n$ $n$ th term of an arithmetic sequence?

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How do I find the $n$ $n$ th term of an arithmetic sequence?

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Answer 1 · 2016-03-25T00:44:39

$a_{n} = a_{1} + (n - 1) \cdot d$ $a_n=a_1+(n-1)*d$
$XXX$ $color(white)("XXX")$ where $a_{1}$ $a_1$ is the first term and
$XXXXXXX d$ $color(white)("XXXXXXX")d$ is the difference between a term and its previous term.

Explanation:

Examine the pattern:

$a_{1}$ $a_1$
$a_{2} = a_{1} + d = a_{1} + 1 d$ $a_color(brown)(2)=a_1+d=color(green)(a_1+1d)$
$a_{3} = a_{2} + d = a_{1} + d + d = a_{1} + 2 d$ $a_color(brown)(3)=a_2+d=a_1+d+d=color(green)(a_1+2d)$
$a_{4} = a_{3} + d = a_{1} + 2 d + d = a_{1} + 3 d$ $a_color(brown)(4)=a_3+d=a_1+2d+dcolor(green)(=a_1+3d)$
$a_{5} = a_{4} + d = a_{1} + 3 d + d = a_{1} + 4 d$ $a_color(brown)(5)=a_4+d=a_1+3d+d=color(green)(a_1+4d)$

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How do I find the $n$ $n$ th term of an arithmetic sequence?

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How do I find the $n$ $n$ th term of an arithmetic sequence?