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Let A_{1}, A_{2}, A_{3} be the three A.P. with the same common difference \mathrm{d} and having their first terms as \mathrm{A}, \mathrm{A}+1, \mathrm{~A}+2, respectively. Let a, b, c be the 7^{\text {th }}, 9^{\text {th }}, 17^{\text {th }} terms of \mathrm{A}_{1}, \mathrm{~A}_{2}, \mathrm{~A}_{3}, respectively such that \left|\begin{array}{ccc}a & 7 & 1 \\ 2 b & 17 & 1 \\ c & 17 & 1\end{array}\right|+70=0.
If a=29, then the sum of first 20 terms of an AP whose first term is c-a-b and common difference is \frac{d}{12}, is equal to

Option: 1

495


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

\quad\left|\begin{array}{ccc}A+6 d & 7 & 1 \\ 21(A+1+8 d) & 17 & 1 \\ A+2+16 d & 17 & 1\end{array}\right|+70=0

A=-7, d=6
\therefore \mathrm{c}-\mathrm{a}-\mathrm{b}=20
\therefore 5_{20}=495

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shivangi.shekhar

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