SOLUTION: given the sum S10=910 of an arithmetic sequence & A20=95, find A1?

Question 1098316: given the sum S10=910 of an arithmetic sequence & A20=95, find A1?
Answer by greenestamps(13215) (Show Source): You can put this solution on YOUR website!

Let a be the first term and d be the common difference.

If the sum of the first 10 terms of an arithmetic sequence is 910, then that sum of 910 is the sum of 5 pairs of numbers, each with a sum of 910/5 = 182. One of those pairs is the sum of the first and tenth numbers.

The first number is a; the 10th number is a+9d: so

The 20th term, 95, is a+19d:

That gives you two equations in a and d which you can solve to find the answer to the problem.

But I'm wondering if you have shown the right numbers, because with the numbers you show, the terms of the sequence turn out to be ugly fractions.

So I'm not going to show the ugly arithmetic; you can solve the pair of equations on your own.
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