The value of x in the geometric sequence is -3.
Option (A) is correct.
To find the value of x.
A progression of numbers with a constant ratio between each number and the one before .A geometric progression is a sequence in which any element after the first is obtained by multiplying the preceding element by a constant called the common ratio which is denoted by r. For example, the sequence 1, 2, 4, 8, 16, 32… is a geometric sequence with a common ratio of r = 2.
Given that:
The geometric sequence are x, 3, -1/3.......
Let x = a be the first term
3 = a*r = x *r , is second term
r is the common ratio,
r =3/x
- 1/3 = ar^2 = x r^2
substitute r, and solve for x:
-1/3 = x*3*3/x*x
cancel out the x term from numerator and denominator we have,
-1/3=9/x
By cross multiplication,
x=-9/3
By simplifies
x=-3
first term is x = -3
So, the value of x in the geometric sequence is -3.
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