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Explicit equations for arithmetic sequences follow a specific format.
$a_{n}=a_{1}+(n−1)d $
In this form, $a_{1}$ is the first term in a given sequence, $d$ is the common difference from one term to the next, and $a_{n}$ is the $nth$ term in the sequence. For this exercise, the first term is $a_{1}=100.$ Let's observe the other terms to determine the common difference $d.$
$100→+10110→+10120→+10130… $
As we can see $d=10.$ By substituting these two values we found into the explicit equation and simplifying, we can find the formula for this sequence.
This equation can be used to find *any* term in the given sequence. To find $a_{10},$ the $10_{th}$ term in the sequence, we substitute $10$ for $n.$
The $10_{th}$ term in the sequence is $190.$

$a_{n}=a_{1}+(n−1)d$

$a_{n}=100+(n−1)(10)$

DistrDistribute $10$

$a_{n}=100+10n−10$

SubTermSubtract term

$a_{n}=10n+90$

$a_{n}=10n+90$

Substitute$n=10$

$a_{10}=10(10)+90$

MultiplyMultiply

$a_{10}=100+90$

AddTermsAdd terms

$a_{10}=190$