Question

can the product of two consecutive terms of a sequence having common difference 2 be -5? can it be -1?​

Answer 1

Answer:

It cannot be -5 , but it can be -1

Step-by-step explanation:

Let the two consecutive terms be a and b,

common difference = b-a = 2 ---equation (1)

In 1st case,

a×b = -5

a = -5/b ---equation (2)

putting (2) in (1)

b + 5/b = 2

b^2 - 2b + 5 = 0

Discriminant D= -16

negative discriminant which means that the roots of this quadratic equation are imaginary.

Since the value of b is not real, we cannot have -5 as product of a and b with the given common difference 2.

In 2nd case,

a×b = -1

a = -1/b ---equation (3)

putting (3) in (1)

b + 1/b = 2

b^2 - 2b + 1 = 0 [ D= 0 which means one real solution ]

(b-1)^2 = 0

b = 1

a = - 1

..in this case, we are getting a real value of b which makes the given condition in the question possible.