JEE Main 2020 · 8 January · evening · Single correct · +4 / −1
If the 10ᵗʰ term of an A.P. is 1/20 and its 20ᵗʰ term is 1/10, then the sum of its first 200 terms is
- (a) 100
- (b) 1001/2
- (c) 501/4
- (d) 50
Answer and solution
Answer (b) 1001/2
Solution
Maths sir · 3 steps
Subtract the two term equations to get d. Then you will see every term is just n/200.
- Find d. Write a + 9d = 1/20 and a + 19d = 1/10. Subtracting gives 10d = 1/20, so d = 1/200.
- Find a. a = 1/20 - 9/200 = (10 - 9)/200 = 1/200. Since a = d, the nth term is aₙ = 1/200 + (n-1)1/200 = n/200.
S₂₀₀ = 200/2(a₁ + a₂₀₀) = 100(1/200 + 1) = 1/2 + 100
- So. S₂₀₀ = 201/2 = 1001/2, which is option (b).
The idea to keep. Two terms of an A.P. give two linear equations in a and d. Subtract them first to get d, then use Sₙ = n/2(first + last).
Answer from the NTA final answer key. Solution by PrepWiser.