JEE Main 2024 · 27 January · evening · Single correct · +4 / −1
The 20ᵗʰ term from the end of the progression 20,19 1/4, 18 1/2, 17 3/4, …,-129 1/4 is :
- (a) -115
- (b) -100
- (c) -110
- (d) -118
Answer and solution
Answer (a) -115
Solution
Maths sir · 4 steps
Turn the AP around: start at the last term and step backwards with the opposite common difference.
- Common difference. Each term drops by 3/4, so d = -3/4. The last term is -1291/4 = -517/4.
- Read from the end. Read backwards, the progression is again an AP. It starts at l = -517/4 and has common difference +3/4.
T₂₀ (from end) = l + 19 × 3/4 = -517/4 + 57/4 = -460/4 = -115
- Check from the front. From -517/4 = 20 + (n-1)(-3/4) we get n - 1 = 199, so there are 200 terms. The 20th from the end is the 181st from the start: 20 + 180 × (-3/4) = 20 - 135 = -115.
- So. The 20th term from the end is -115, which is option (a).
The idea to keep. The rth term from the end of an AP is l - (r-1)d. Start from the last term and move back r-1 steps. You do not need to count the terms first.
Answer from the NTA final answer key. Solution by PrepWiser.