Sequences And Series Question 4
Question 4 - 25 January - Shift 1
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 $7^{\text{th }}, 9^{\text{th }}, 17^{\text{th }}$ terms of $A_1, A_2, A_3$, respectively such that $ \begin{vmatrix} a & 7 & 1 \\ 2 b & 17 & 1 \\ c & 17 & 1\end{vmatrix} +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
Show Answer
Answer: 495
Solution:
Formula: General Term of an AP and Sum of $\mathbf{n}$ terms of an AP,
$ \begin{vmatrix} A+6 d & 7 & 1 \\ 2(A+1+8 d) & 17 & 1 \\ A+2+16 d & 17 & 1\end{vmatrix} +70=0$
$\Rightarrow A=-7$ and $d=6$
$\therefore c-a-b=20$
$S _{20}=495$
