I'm currently learning arithmetic sequences, and I've gotten to the means. I'm answering an activity as a test to see if what I'm doing is right.

Here's an example through format:

First term = 10
Last term = 40
Arithmetic means = 5
Answer = {15, 20, 25, 30, 35}

I'm sure means work that way, even though I didn't research about it. Since I'm not that good with algebra, I'm having trouble handling this one:

First term =  x + y
Last term = 4x - 2y
Arithmetic means = 2

If not the full answer, can you at least give me a simple way to get it? The concept of $\sum$ still confuses me, so if you give me some answer using that, please explain it.

Revision

Alright, let's fix the question. What does an "arithmetic mean" mean? According to the book, it's the set of terms in order that are between the first and the last terms given which creates an arithmetic sequence.

If that's so, let's use the example with a correct answer:

First term = 10
Last term = 40
No. of arithmetic means = 5 (I should've pointed it out)
Answer = {15, 20, 25, 30, 35}
Arithmetic sequence = {10, 15, 20, 25, 30, 35, 40}
Common difference = 5

Let's try another with an example I thought of that's not in the book:

First term = 16
Last term = 72
No. of arithmetic means = 3
Answer = {30, 44, 58}
Arithmetic sequence = {16, 30, 44, 58, 72}
Common difference = 14

See what I mean?

Back to the original question, I can't figure out how to put $x$ and $y$ in this:

First term = x + y
Last term = 4x - 2y
No. of arithmetic means = 2
Answer = ?
(Current) arithmetic sequence = {x + y, ?, ?, 4x - 2y}
Common difference = ?

I might figure this out on my own; this has been hurting my head for a while now. I'll let you guys know.

posted almost 2 years ago

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2y ago

General Sebast1an‭

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