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

In summary, to find the smallest positive term of an arithmetic series, you can rearrange the formula S_n=\frac{n[2a_1+(n-1)d]}{2}, where n is the number 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.
  • #1
CathyLou
173
1
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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  • #2
You could rearrange the formula [tex] S_n=\frac{n[2a_1+(n-1)d]}{2} [/tex], 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.
 
  • #3
cristo said:
You could rearrange the formula [tex] S_n=\frac{n[2a_1+(n-1)d]}{2} [/tex], 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
 

What is an arithmetic series?

An arithmetic series is a series of numbers where the difference between consecutive terms is a constant value. It can be represented by the formula Sn = a + (a + d) + (a + 2d) + ... + (a + (n-1)d), where a is the first term and d is the common difference.

How do you find the sum of an arithmetic series?

The sum of an arithmetic series can be found using the formula Sn = n/2 * (a + l), where n is the number of terms, a is the first term, and l is the last term.

What is the formula for the nth term of an arithmetic series?

The formula for the nth term of an arithmetic series is tn = a + (n-1)d, where a is the first term and d is the common difference.

What is the common difference in an arithmetic series?

The common difference in an arithmetic series is the constant value that is added to each term to get the next term in the series.

How do you determine if a series is arithmetic or not?

To determine if a series is arithmetic, you can check if the difference between consecutive terms is constant. If the difference is the same for all terms, then the series is arithmetic. You can also use the formula tn = a + (n-1)d to check if the series follows the pattern of an arithmetic series.

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