The sum of positive terms of the series 10+9 (4)/(7)+9 (1)/(7)+…is (A) (352)/(7) (B) (437)/(7) (

step 1 Note that this is an arithmetic series and the first term equals 10, which is 70 over 7. And a c

The sum of positive terms of the series 10+9 (4)/(7)+9...

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Key Concepts

Sum of an Arithmetic Series

The sum of the first n terms of an arithmetic progression is given by S? = n/2 × (a? + a?). This formula allows one to calculate the total sum of a specified number of terms in the sequence by using the average of the first and last terms multiplied by the number of terms.

Determining the Number of Terms Using Inequalities

When dealing with arithmetic sequences where only terms satisfying a certain condition (like being positive) are considered, one must use inequalities to determine the maximum number of terms that meet the criteria. This involves solving a? > 0 in conjunction with the nth term formula.

Arithmetic Progression

An arithmetic progression (AP) is a sequence in which each term after the first is generated by adding a fixed constant, known as the common difference, to the preceding term. This concept is fundamental in understanding series where terms follow a consistent linear pattern.

Nth Term Formula

The nth term of an arithmetic progression can be found using the formula a? = a? + (n ? 1)d, where a? is the first term and d is the common difference. This formula is essential to determine any term in the sequence, including identifying when terms become non-positive.

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