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Let A_1,A_2,A_3 be the three A.P. with the same common difference d and having their first terms as A,A+1,A+2, respectively. Let a,b,c be the 7^ th…

JEE Main 2023 — Mathematics Algebra

2023integermedium

Let A1,A2,A3{A}_{1},{A}_{2},{A}_{3}A1​,A2​,A3​ be the three A.P. with the same common difference ddd and having their first terms as A,A+1,A+2A,A+1,A+2A,A+1,A+2, respectively. Let a,b,ca,b,ca,b,c be the 7th ,9th ,17th {7}^{\text{th }},{9}^{\text{th }},{17}^{\text{th }}7th ,9th ,17th  terms of A1,A2,A3{A}_{1},{A}_{2},{A}_{3}A1​,A2​,A3​, respectively such that ∣a712b171c171∣+70=0|\begin{matrix}a & 7 & 1 \\ 2b & 17 & 1 \\ c & 17 & 1\end{matrix}|+70=0∣a2bc​71717​111​∣+70=0. If a=29a=29a=29, then the sum of first 202020 terms of an AP whose first term is c−a−bc-a-bc−a−b and common difference is d12\frac{d}{12}12d​, is equal to _____ .

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Held on 25 Jan 2023 · Verified 6 Jul 2026.

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