Option D) is correct. The equation representing the above sequence is f(x) = f(x-1) - 6.
According to the question we have been the sequence
2, -4, -10, -16,.......
Here, a₁ = 2 a₃ = -10
a₂ = -4 a₄ = -16
Thus, difference between the first two terms is:
d = a₂ - a₁
= -4 - 2 = -6
Similarly difference between the second third term is :
d = a₃ - a₂ = -10 - (-4) = -10 + 4 = -6
We will see that the difference between the terms is constant that is
d = -6
We know that , aₙ = aₙ₋₁ + d
putting the value of d in the above formula we get
aₙ = aₙ₋₁ + (-6)
aₙ = aₙ₋₁ -6
Also can be written as :
f(x) = f(x-1) - 6
That is option D) is correct. The equation representing the above sequence is f(x) = f(x-1) - 6.
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