When the first four terms in an arithmetic sequence are x+y, x-y, xy and x÷y, then the fifth term will be
A sequence of numbers in which every term (except the first term) is obtained by adding a constant number to the previous term is called an arithmetic sequence
In given arithmetic sequence
The first term = x+y
The second term = x-y
Then, the common difference= (x-y)-(x+y)
x-y-x-y= -2y
The third term = x-y+(-2y)
x-y-2y= x-3y
In question third term is given as xy
So both are equal
x-3y=xy
-3y=xy-x
-3y=x(y-1)
x=
Similarly fourth term will be
x-3y-2y=x-5y
substitute the value of x in the equation
Split the middle term and factorize it
(y-1)(5y+3)=0
y cannot be equal to 1, because the third term and fourth term will become x.
substitute the value of y in the equation of x
The fifth term=
Hence, when the first four terms in an arithmetic sequence are x+y, x-y, xy and x÷y, then the fifth term will be
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