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QuestionFind the formula for the sequence {−8,−6,−4,−2,…}\{-8,-6,-4,-2, \ldots\}. Options: an=2n−10a_{n}=2n-10, an=−8n+2a_{n}=-8n+2, an=n+2a_{n}=n+2, an=n−2a_{n}=n-2.

Studdy Solution

STEP 1

Assumptions1. The sequence given is an arithmetic sequence. . The common difference between the terms is constant.
3. The sequence starts with -8 and increases by each term.

STEP 2

First, we need to identify the common difference in the sequence. The common difference in an arithmetic sequence is the difference between any two successive terms.d=an+1−and = a_{n+1} - a_{n}

STEP 3

Now, plug in the given values for the first and second term of the sequence to calculate the common difference.
d=−6−(−8)d = -6 - (-8)

STEP 4

Calculate the common difference.
d=−6−(−8)=2d = -6 - (-8) =2

STEP 5

Now that we have the common difference, we can use the formula for the nth term of an arithmetic sequence to find the formula for the given sequence. The formula for the nth term of an arithmetic sequence isan=a1+(n−1)⋅da_{n} = a_{1} + (n-1) \cdot dwhere- ana_{n} is the nth term- a1a_{1} is the first term- nn is the term number- dd is the common difference

STEP 6

Plug in the values for the first term and the common difference into the formula.
an=−8+(n−1)⋅2a_{n} = -8 + (n-1) \cdot2

STEP 7

implify the formula.
an=−+2n−2a_{n} = - +2n -2

STEP 8

Combine like terms.
an=2n−10a_{n} =2n -10So, the formula for the given sequence is an=2n−10a_{n}=2n-10.

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