JEE Advanced 2022 Sequences & Series: Find T30 by Telescoping (Q10) #maths #jee #jeeadvanced #exam

JEE Advanced 2022 sequences and series, Paper 1 Q10, solved step by step: a₁, a₂, a₃, … is an AP with a₁ = 7 and common difference 8, T₁ = 3 and T(n+1) − T(n) = a(n). Is T₂₀ = 1604? Is the sum of the first 20 terms 10510? Is T₃₀ = 3454? Is the sum of the first 30 terms 35610? A telescoping sum turns T(n) into a simple quadratic. JEE Advanced is the second-stage entrance exam for the Indian Institutes of Technology (IITs). This question is from Paper 1 (2022) and is a multiple-correct question: one or more of the options (A)–(D) can be true, so you have to check every option. In this video: • The AP formula a(n) = 8n − 1 • Telescoping: adding up the differences T(n+1) − T(n) • A closed form T(n) = 4n² − 5n + 4 • Checking T₂₀ and T₃₀ • Summing T(k) with the formulas for Σk and Σk² • A check by building the sequence term by term • A staircase visual: why T(n) follows a parabola • Two common mistakes and the correct approach ⏸ Pause at 0:24 and try it yourself before watching the solution! Chapters: 0:00 JEE Advanced 2022 Q10: the question 0:13 Problem statement & pause to try 0:29 The AP and telescoping 0:52 Closed form for T(n) 1:05 Checking T20 and T30 1:18 Checking the sums & final answer 1:37 Check: building the sequence 1:48 Visualization: staircase of differences 2:08 Common mistakes 2:24 Summary & next question (Q11) ▶ Previous video (Q9):    • JEE Advanced 2022 Definite Integral: How M...   💬 Next up is Q11: two planes P₁ and P₂ and four lines. Which of them can be an edge of a tetrahedron with two faces on P₁ and P₂? Comment your pick! Source: JEE Advanced 2022, Paper 1, Question 10 (Mathematics). Answer: (B) and (C). #maths #mathematics #math #mathstricks #jee #jeeadvanced #jeepreparation #exam #education #learning