Question

1

Jenny is arranging rows of chairs for the student play.
There are 7 chairs in the first row.
Each row behind the first row has two more chairs than the previous row.
Complete the explicit definition for this sequence. Your answer must be fully simplified.
Explicit Definition of an Arithmetic Sequence
an = a1 + (n-1) d

Answer 1

Answer:
`a_n = 2n+5`

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Work Shown:

`a_n = a_1 + d(n-1)\\\\a_n = 7 + 2(n-1)\\\\a_n = 7 + 2n-2\\\\a_n = 2n+5\\\\`

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Step-by-step explanation:

We plug in
`a_1 = 7 \ \text{ and } \ d = 2` as they represent the first term and common difference in that order. The common difference is 2 because the number of chairs increases by 2 each time you move up a row.

To verify that answer, let's plug in the value n = 1

`a_n = 2n+5\\\\a_1 = 2(1)+5\\\\a_1 = 2+5\\\\a_1 = 7\\\\`

Which matches with the first term being 7. I'll let you verify other terms.