If the 10^th term of an A.P. is (1)/(20) and its 20^th term is (1)/(10), then the sum of its f

step 1 In this question it is given that 10th term equal 1 by 20 and 20th term equals 1 by 10, then we

If the 10^th term of an A.P. is (1)/(20) and its 20^th ...

If the $10^{\text {th }}$ term of an A.P. is $\frac{1}{20}$ and its $20^{\text {th }}$ term is $\frac{1}{10}$, then the sum of its first 200 terms is:
(a) 50
(b) $50 \frac{1}{4}$
(c) 100
(d) $100 \frac{1}{2}$

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Key Concepts

Solving Linear Equations

When values of specific terms are provided, setting up linear equations from the nth term formula allows determination of unknown variables such as the first term and the common difference. Solving these simultaneous equations is a fundamental algebraic technique applied in arithmetic progressions.

Sum of an Arithmetic Progression

The sum of the first n terms of an arithmetic progression is found using the formula S_n = n/2 [2a + (n-1)d]. This formula aggregates the sequence's terms efficiently and is used when the number of terms, the first term, and the common difference are known.

Arithmetic Progression

An arithmetic progression (AP) is a sequence in which the difference between successive terms is constant. This constant difference (d) defines the progression and allows for the development of general formulas to find any term in the sequence as well as the sum of a finite number of terms.

nth Term Formula

The nth term of an arithmetic progression can be expressed as a + (n-1)d, where a is the first term and d is the common difference. This formula is essential for relating terms in the sequence and finding unknown parameters when specific term values are given.

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