Finding the First Term and Common Difference of an Arithmetic Series

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To find the first term and common difference of the arithmetic series, the equations for the sum of the first n terms are applied. Given that the sum of the first 4 terms is -8 and the sum of the first 5 terms is 85, two equations can be set up using the formula Sn = n/2 (2a + (n-1)d). Solving these equations simultaneously reveals the values for the first term (a) and the common difference (d). The calculations lead to the conclusion that the first term is -12 and the common difference is 5. This solution effectively demonstrates the application of arithmetic series formulas in problem-solving.
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Homework Statement



The sum of the first 4 terms in an arithmetic series is -8 and the sum of the first 5 terms is 85. Determine the first term and the common difference.

Homework Equations



tn = a + (n-1)d
Sn = n/2 (2a + (n-1)d)

The Attempt at a Solution

 
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Blister said:

The Attempt at a Solution


I think you forgot to type in this section.
 

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