Finding the Smallest Positive Term in an Arithmetic Series (C1 Level)

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To find the smallest positive term in an arithmetic series, one can rearrange the formula S_n = n[2a_1 + (n-1)d]/2, where S_n represents the sum of the first n terms, n is the number of terms, a_1 is the first term, and d is the common difference. This formula allows for the calculation of terms in the series based on the initial term and the common difference. Understanding how to manipulate this equation is crucial for determining specific values within the series. The discussion emphasizes the importance of recognizing the components of the formula for effective problem-solving. Mastery of this formula is essential for success at the C1 level in mathematics.
CathyLou
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Please could someone tell me the way to find the smallest positive term of an arithmetic series (C1 level) as I cannot find a formula anywhere.

Thank you.

Cathy
 
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You could rearrange the formula S_n=\frac{n[2a_1+(n-1)d]}{2}, where n is the numbers of terms, Sn is the sum of the first n terms, d is the difference between the ith and (i+1)th term, and a1 is the first term of the series.
 
cristo said:
You could rearrange the formula S_n=\frac{n[2a_1+(n-1)d]}{2}, where n is the numbers of terms, Sn is the sum of the first n terms, d is the difference between the ith and (i+1)th term, and a1 is the first term of the series.

Okay. Thanks for your help.

Cathy
 

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