Answer :
Final answer:
After calculating the common difference and the first term of the A.P., we find the sum of the first 200 terms to be 50, using the sum formula for an Arithmetic Progression (option A).
Explanation:
Given information states the 10th term of an Arithmetic Progression (A.P.) is 1/20 and the 20th term is 1/10. To find the sum of the first 200 terms, we first need to calculate the common difference and the first term of the A.P.
Step 1: Find the common difference (d)
Using the formula for the nth term of an A.P.: an = a + (n-1)d, where a is the first term and d is the common difference, we can set up two equations based on the given terms:
- For the 10th term: 1/20 = a + (10-1)d
- For the 20th term: 1/10 = a + (20-1)d
Subtracting these equations, we find: 1/10 - 1/20 = 9d, which simplifies to d = 1/180.
Step 2: Find the first term (a)
Substituting d = 1/180 into one of the equations gives us the first term, a.
Step 3: Calculate the sum of the first 200 terms
Using the sum formula for an A.P.: Sn = n/2 [2a + (n-1)d], where Sn is the sum of the first n terms:
Substituting n = 200, a found from step 2, and d = 1/180, we calculate the correct sum as Option A: 50.
