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- anonymous

The fifth term of an arithmetic progression is 28 and the tenth term is 58.
Find the first term and the common difference.
Please help! I tried 58=28+4d but that didn't work.

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- anonymous

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- anonymous

Do you have options?

- anonymous

I am sorry I don't really know what you mean?

- anonymous

Sorry! I meant, is it multiple choice?

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- anonymous

Oh! No it isn't. But I do have the answers:
d=6 first term=4

- anonymous

I just don't know how they got there. I have been taught some equations to work out the sum of a arithmetic series, to find the number of terms and so on but I don't know how to apply them here.

- anonymous

So one thing to note (if you don't know this) with arithmetic patterns, it works in the way that they always add the same thing to get to each number.

- anonymous

Yes

- anonymous

1. 4
2. ?
3. ?
4. ?
5. 28
What number can you continue to add 3 times and get to 28 from four? (I know the answer, but I want you to understand it :) )

- anonymous

Well, I understand the concept but actually I am not sure how to figure it out except for trail and error, is that how you are meant to figure it out?

- anonymous

If I subtract four from 28 then divide the answer by four I get 6. But I don't know if that is just chance

- anonymous

Well, because these are such small numbers, yes. Trial and error would be the best. And yep! 6 is correct! And if you're worried it's just a coincidence, then you can do it all the way up through 58 and it will work! See: 4, 10, 16, 22, 28, 34, 40, 46, 52, 58. Tada! :D

- anonymous

Yay! Ok so I do I know without having the first number, and is there an equation for it?

- anonymous

Well the equation would be x + 6. And, without the first number, you could have just done it from 28 to 58: 28, 34, 40, 46, 52, 58. 6 Would still be the only number that would work. :)

- anonymous

Ok, how would I find the first term now? Would I use a + (k-1)d and rearrange to find a = (k-1)d ?

- anonymous

I honestly don't know how I would make an equation to show it, but you can simply subtract 6 from 28 repeatedly until you get to what would be the first term. 4th: 22 3rd: 16 2nd: 10 1st: 4 I'm sorry I don't know the actual equations though! :(

- anonymous

No thats ok, that makes sense and it works so no problem. How practical would that be for larger numbers though?

- anonymous

Well, if you have a calculator, it would be just as simple. And I would still use it, as long as they didn't go up into the millions. Is this a homework assignment? Or do you do online school?

- anonymous

Ok, just making sure! No, I am home-schooled. I find this site super helpful as often I find myself stuck on really little things which I have looked at for so long that I can't see my mistake anymore! Or just to easily find an equation I have missed or something. Thank you very much for your help, much appreciated.

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