Q If an=aaa a⏟n digits and 6n8n042n=xy0z, then A - Maths - Matrices

Question

Q   I f   a n = a a a a ⏟ n   d i g i t s
  a n d   6 n 8 n 0 4 2 n = x y 0 z ,   t h e n
  A   x 2 + y = z B   x 2 + y = 2 z C   x 2 + y
+ z = 0 D   x 2 + y + 2 z = 0

Aarushi Mishra · Accepted Answer

an=aaa n timesaaaaa
n times=a×10n-1+a×10n-2+a×10n-3+
+a×10n-n=a×10n-1+10n-2+
+1It is sum of G P
 with first term=a and r=110=10-1Sum of G
P
=arn-1r-1=a10n-110-1n-110-1-1=a10n-110-n-1110-1=a10n-1-n-10n-11-1010=a10-1-10n-1-910=a×1010-1-10n-1-9=a1-10n-9an=a10n-196n=610n-198n=810n-1942n=4102n-19=410n2-129=410n-110n+196n8n042n=xy0z610n-19810n-190410n-110n+19=xy0zComparingx=610n-19y=810n-19z=410n-110n+19x2+y=3610n-192+810n-19=10n-193610n-19+8=10n-191210n-13+8=410n-19310n-13+2=410n-1910n-1+2=410n-1910n+1=zx2+y=z

Q . I f a n = a a a . . . . . . . . . . a ⏟ n d i g i t s a n d 6 n 8 n 0 4 2 n = x y 0 z , t h e n A . x 2 + y = z B . x 2 + y = 2 z C . x 2 + y + z = 0 D . x 2 + y + 2 z = 0