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# Arithmetic Series

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Let a1, a2, a3, ..., a10, a11, a12 be an arithmetic sequence. If a1 + a2 = 4 and a2 + a3 = 5, then find a1.

Mar 13, 2024

#1
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Let a1, a2, a3, ..., a10, a11, a12 be an arithmetic sequence. If a1 + a2 = 4 and a2 + a3 = 5, then find a1.

a1 + a2 = 4   &   a2 + a3 = 5

Since it's an arithmetic sequence, the difference between adjacent terms is the same.

Call that difference, i.e., the increment, let's call it "n".  Just keep this in mind for a while.

a2 + a3 = 5

a1 + a2 = 4

Subtract one from the other

a3 – a1 = 1

Since a3 is (a1 + n + n)

(a1 + n + n) – a1 = 1

2n = 1  therefore n = 0.5

Referring back to the top

a1 + a2 = 4

a2 = (a1 + 0.5) so plug it in

a1 + (a1 + 0.5) = 4

2a1 + 0.5 = 4

2a1 = 4 – 0.5 = 3.5

a1 = 3.5 / 2

a1 = 1.75

a1 = 1.75

a2 = 2.25        a1 + a2 = 4

a3 = 2.75        a2 + a3 = 5

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Mar 14, 2024
#3
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"Liliam0216" is a bot and therefore will not be able to figure out which two of your generally unecessary steps are not needed.

Mar 15, 2024
edited by Holtran  Mar 15, 2024