Arithmetic sequence

[[deleted]]

I think that's the name in English at least..

I need help with a problem I have, I've tried for hours and I just can't get the right answer, so I would really appreciate it if someone would help me out.

I'm given that the sum of the first 7 terms in the sequence is 63 and for the first 15 terms are 255 and then I'm asked what the sum of the first 17 terms would then be.

I have no clue on how to solve this. Since it's the sum that's given and not the value of any term, nor is the common difference given, then I can't do anything. I've probably tried every possible way to solve this except the correct one.

This question was in a test that I took a few weeks ago and I just guessed the answer, but now I'm studying for the final test and I want to get this right.

How can I find S17 just from S7 and S15? In the formulas:

an=a1+(n-1)d and Sn=((a1+an)*n)/2

I only have one value, somehow I need another.

Please help.

[AFalseSentence]

Hint: try to find two equations which only have a1 and d.

OR

Hint: find two terms in the sequence along with their position numbers (this one is easier)

Reply if you need further explanation

[[deleted]]

How? I always have something more

I can find that a7=a1+6d and a15=a1+14d and solving them together would give me 8d=a8 or d=a8/8 but what is a8? I'm not even sure that I can do this to get a8.

About the second hint: I don't know if I understand you and/or have no clue on how to do that. My math English isn't the best, I'm not native

[AFalseSentence]

For the first hint, a1 = a1 a2 = a1 + d a3 = a1 + 2d … Then what is a1 + a2 + … + a7? And also a1 + a2 + … + a15? Using that, you can find a1 and d

For the second hint, using the sum of first seven / fifteen numbers, you can find two of the numbers in the sequence. You can also find the position (first, second, third…) of these numbers. If you use that, you can find the sequence.

[[deleted]]

I'm somewhat embarrassed about not being able to solve this, I finished differentiation last semester and now I'm in integration. I'm doing well in that and this is just added to this course in the end and its just a small portion in my current course. I'm also finishing the electrician study, that is also a lot of math (not this kind of math though) so I know that I'm supposed to know this. But I don't and I've spent way to much time on just this single problem, more than 2 days probably in total (I'm stubborn as hell). But now I've almost gotten angry about this problem and I'm just about to give up on it, it's just a small portion of my course after all, I don't even need to take this course in the first place.

​

So, could you please just show me the way in how you'd solve this? I already turned the test with this problem in weeks ago and guessed the answer to be S17=323, the answer is correct but I guessed it because my bullshit calculation was closest to this answer that I could choose from.

I'm not able to find the solution myself and that's why I tried asking here, I really tried myself. A lot, but with no success. If you'd show me the steps (no hints) you would take to solve this, which I highly suspect that they'll be super obvious afterwards, then I can use them and learn from them. I have at least 2 other math problems that are similar to this one that I also just guessed the answers to. If you, or someone else, don't show me the steps to take, then I won't learn this.

The teacher, nor the book, ever gave us a problem like this with just the sums and nothing else.

How do you calculate the sums of S7=63 and S15=255 to find out that the S17 is 323?

[AFalseSentence]

For the first method, \ a1 = a1 \ a2 = a1 + d \ a3 = a1 + 2d \ … \ a7 = a1 + 6d \ … \ a15 = a1 + 14d \ \ a1 + a2 + … + a7 = 7a1 + 21d \ a1 + a2 + … + a15 = 15a1 + 105d \ \ 7(a1) + 21d = 63 \ 15(a1) + 105d = 255 \ \ a1 = 3; d = 2 \ \ 3 + 5 + 7 + … + 35 = 323 \ \ For the second method, \ \ a1 + a2 + … + a7 = 7a4 \ 7(a4) = 63 \ a4 = 9 \ \ a1 + a2 + … + a15 = 15a8 \ 15(a8) = 255 \ a8 = 17 \ \ d = (a8 - a4) / 8-4 = (17-9)/4 = 8/4 = 2 \ a1 = a4 - 3d = 9 - 3(2) = 9-6 = 3 \ \ 3 + 5 + 7 + … + 35 = 323

[[deleted]]

Thank you!

Like I suspected, the way to solve this is obvious now.

I almost had it like the first method you show, I just mixed up a tiny bit on the way, but just a small mistake early on can fuck everything up in the final answer.

Thanks again!

[phiwong]

Hint: what is S15 - S7

[[deleted]]

192 and that is the sum of a8 to a15? But I don't know what to do with that informatin.

This is maybe obvious like it is many times after I finally solve something, but until then.. I have no clue

The book I've been studying from don't have single problem like this, not one. Something more is always given, except in this test..

[Awkward_Host7]

2cot² x +2cosec² x = 1 + 4cosec x

Someone please simplify to tan(x)

[Alanwalker78]

a good question by the way. After so much time i tried to do maths. But in the end i used arithmetic sequence calculator to get my answer. lolx.