SOLUTION: Hi i need help for this question can anyone help me... In an arithmetic sequence, the sum of the first term term is 125 and the third term is 5. How to find the first term and t

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Question 825175: Hi i need help for this question can anyone help me...
In an arithmetic sequence, the sum of the first term term is 125 and the third term is 5. How to find the first term and the common difference?
Thanks for helping mates ^_^

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
You are missing something. Your post does not explain what is the meaning of the number 125 you mention.
The "sum of the first term term" is like the sound of one hand clapping.
You need two hands to clap and you need to have at least two terms to add together to have a sum.

a%5B1%5D= the first term
d= common difference
a%5Bk%5D= term number k
S%5Bn%5D= sum of the first n terms
You can calculate any term number k from k, the first term, and the common difference:
a%5Bk%5D=a%5B1%5D%2B%28k-1%29d .
You can calculate the sum of the first n%7D%7D+term+from+%7B%7B%7Bn, the first term, and the common difference:
S%5Bn%5D=n%282a%2B%28n-1%29d%29%2F2 .
Having n, the sum of the first n terms, k, and the value of term number k, you can set up the two equations above and solve for a%5B1%5D and d .