Question

What is the explicit formula for the sequence?
7, 2, –3, –8, –13, . . .

Answer 1

Answer: Choice A,
`a_n = -5n+12`

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Step-by-step explanation:

`a_1 = 7` is the first term

`d = -5` is the common difference, telling us to add -5 to each term to get the next term. This is the same as subtracting 5 from each term

The nth term of the arithmetic sequence is,

`a_n = a_1 + d(n-1)\\\\a_n = 7 + (-5)(n-1)\\\\a_n = 7-5(n-1)\\\\a_n = 7-5n+5\\\\a_n = -5n+12\\\\`

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As a check, let's plug in n = 4 and we should get -8 as our fourth term

`a_n = -5n+12\\\\a_4 = -5(4)+12\\\\a_4 = -20+12\\\\a_4 = -8\\\\`

so that confirms that portion of the sequence. I'll let you check the other values.