Question

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.

Answer 1

Do you have options?

Answer 2

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

Answer 3

Sorry! I meant, is it multiple choice?

Answer 4

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

Answer 5

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.

Answer 6

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.

Answer 7

Yes

Answer 8

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 :) )

Answer 9

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?

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

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. :)

Answer 14

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

Answer 15

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! :(

Answer 16

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

Answer 17

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?

Answer 18

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.