Let A1,A2,A3 be the three series in AP, with same common difference ‘d’ and their first terms A,A+1,A+2are if a, b, c are 7th, 9th, 17th terms A1,A2,A3 of such that|a712b171c171|+70=0If a=29 then sum of first 20 terms of an AP where first term c –a = b with common difference d12 is

|A+6d712(A+1+8d)171A+2+16d171|+70=0⇒A=−7 and d=6c−a−b=20Sn=n2 [2a+(n−1)d]=10[40+19(12)]=5[80+19]=5(79)=495

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Let $A_{1}, A_{2}, A_{3}$ be the three series in AP, with same common difference ‘d’ and their first terms $A, A + 1, A + 2$ are if a, b, c are 7th, 9th, 17th terms $A_{1}, A_{2}, A_{3}$ of such that
$| \begin{matrix} a & 7 & 1 \\ 2 b & 17 & 1 \\ c & 17 & 1 \end{matrix} | + 70 = 0$
If $a = 29$ then sum of first 20 terms of an AP where first term c –a = b with common difference $\frac{d}{12}$ is

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answer is 495.

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Detailed Solution

$\begin{array}{l} | \begin{matrix} A + 6 d & 7 & 1 \\ 2 (A + 1 + 8 d) & 17 & 1 \\ A + 2 + 16 d & 17 & 1 \end{matrix} | + 70 = 0 \\ \Rightarrow A = - 7 a n d d = 6 \\ c - a - b = 20 \\ S_{n} = \frac{n}{2} [2 a + (n - 1) d] \\ = 10 [40 + 19 (\frac{1}{2})] \\ = 5 [80 + 19] \\ = 5 (79) \\ = 495 \end{array}$