Question

Match the statements in List 1 with those in List 2

	List 1		List 2
A.	$S_n=54+51+48+...n$ terms $=513$ Value of $n=?$	1.	$20$
B.	$21,42,63,84,......t_n=420,valueofn=?$	2.	$18$
C.	$3,3.6,4.2,4.8,....$ $t_{26}=?$	3.	$32$
D.	$0.5,1,2,4,....$ $t_7=?$	4.	$19$
		5.	$40$

[Note: Here $z$ takes the values in the complex plane and $Im$ $z$ and $Re$ $z$ denote, respectively, the imaginary part and the real part of $z$]

• A. $A-2,4B-1,C-2,D-3$
• B. $A-2,4B-1,C-3,D-1$
• C. $A-2,4B-1,C-1,D-3$
• D. $A-2,4B-1,C-3,D-3$

Answer 1

The correct option is A $A-2,4B-1,C-2,D-3$

(A) $S_n=513$
$\frac{n}{2}\left[2\right(54)+(n-1\left)\right(-3\left)\right]=513$
$n(108-3n+3)=1026$
$n^2-37n+342=0$
$n^2-19n-18n+342=0$
$n(n-19)-18(n-19)=0$
$(n-18)(n-19)=0$
$n=18$ or $n=19$
(B) $t_n=420$
$21+(n-1)21=420$
$1+n-1=20$
$n=20$
(C) $T_{26}=3+(26-1)(0\cdot 6)=3+25(0\cdot 6)=3+15=18$
(D) $t_7=\frac{1}{2}(2{)}^{7-1}=\frac{2^6}{2}=2^5=32$