Question

do it fast with explaination

Answer 1

here we use property of determinant ,

step 1 :- Row1 - Row2 put in Row 1

then , you see all elements of row1 = -1

step 2 :- Row 3 - Row 2 put in Row 3
you see
-2 + 1/a
-3 + 1/b
-4 + 1/c in the 3rd row

Step 2 :- here put row 3 in two part
in this ways two determinant , found
see this in figure . first determinant will be zero

step 4 :- solve 2nd determinant

1( 2016/c -2017/b) - ( 2015/c -2017/a) + ( 2015/b -2016/a ) = 0

1/c -2/ b + 1/ a = 0

2/b = 1/a + 1/c

hence, 1/a , 1/b and 1/c are in AP
so,
a, b , c are in HP

Answer 2

Answer:

hence, 1/a , 1/b and 1/c are in AP

so,

Option d ) a, b , c are in HP