Question

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)

Answer 1

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