Final answer:
To find the first term of an arithmetic series, we can use the formula a1 = a10 - 9d, where a1 is the first term, a10 is the tenth term, and d is the common difference. In this case, S10 is given as 635 and a1 is given as 113. Plugging in these values, we can solve for a10, and then use the formula to find a1.
Step-by-step explanation:
In an arithmetic series, each term is obtained by adding a common difference to the previous term. The sum of the first n terms of an arithmetic series is given by the formula:
Sn = n/2(a1 + an)
where Sn is the sum of the first n terms, a1 is the first term, and an is the nth term. We are given that S10 = 635 and a1 = 113. Plugging these values into the formula, we get:
635 = 10/2(113 + a10)
Simplifying this equation gives:
317.5 = 113 + a10
Subtracting 113 from both sides of the equation, we find that a10 = 204.5. Since an arithmetic series has a constant difference between terms, we can find the first term, a1, by subtracting 9 times this difference from a10:
a1 = a10 - 9d = 204.5 - 9d
Therefore, a1 = 204.5 - 9d.