Given:
The sequence is
1, 4, 16, 64
To find:
The general term of the given sequence.
Solution:
We have, the sequence
1, 4, 16, 64
Here, the ratio between two consecutive terms is same. So, it is a geometric sequence.
First term is:
Common ratio is:
The nth term of a geometric sequence is
...(i)
Where, a is the first term and r is the common ratio.
Putting a=1 and r=4 in (i), we get
Therefore, the general term of the given sequence is .
The expression which represents the other factor, or factors, of the given polynomial is option (C) (2x-1)(x+1)
A cubic equation in algebra is a one-variable equation of the form ax3+bx2+cx+d=0 where an is nonzero. The roots of the cubic function defined by the left side of this equation are the solutions to this equation.
Given expression 2x³-3x²-3x+2 whose one of factor is (x-2)
We have to find second factor of given equation
First we will be rational root theorem to given expression so will get following expression:
So one factor is (x-1) and now simplifying we get 2x² - 5x +2 and the factor of 2x² - 5x +2 will be (2x-1)(x-2)
Hence the expression which represents the other factor, or factors, of the given polynomial is option (C) (2x-1)(x+1)
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