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What is the explicit formula for this arithmetic sequence?-10, -17, -24, -31, ...A. an = -10 + (n - 1)7B. an= -7 + (n - 1)(-10)C. an= -10 + (n - 1)(-7)D. an = 10 + (n - 1)(-7)

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EXPLANATION

Given the arithmetic sequence -10, -17, -24, -31, ...

First we need to apply the constant difference formula:


a_n=a_1+(n-1)d

Checking wheter the difference is constant:


-17-\mleft(-10\mright)=-7,\: \quad \: -24-\mleft(-17\mright)=-7,\: \quad \: -31-\mleft(-24\mright)=-7
\mathrm{The\: difference\: between\: all\: of\: the\: adjacent\: terms\: is\: the\: same\: and\: equal\: to}
d=-7
\mathrm{The\: first\: element\: of\: the\: sequence\: is}
a_1=-10
a_n=a_1+\mleft(n-1\mright)d
\mathrm{Therefore,\: the\: }n\mathrm{th\: term\: is\: computed\: by}\:
d=-7,\: a_n=-7\mleft(n-1\mright)-10
\mathrm{Refine}
d=-7,\: a_n=-7n-3

Hence, the arithmetic sequence is as follows;


a_n=-7\mleft(n-1\mright)-10

The appropiate option is OPTION C

User Yuli
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