Question

What is a possible value for the missing term of the geometric sequence? 50, ___, 450,

Answer 1

Answer:

Geometric sequence states that a sequence in which a number that follows the pattern were the next term is found by multiplying the constant common ratio term(r).

For the sequence: $a, ar, ar^2, ar^3,.....$

The formula for the nth geometric sequence is given by:

$a_n =ar^{n-1}$

where

a is the first term

r is the common ratio

n is the number of terms.

Given that:

A geometric sequence:

50, _$a_2$___, 450

Here, a = first term = 50

$a_3 = 450$

Using the nth geometric sequence formula:

$a_3 = ar^2$

or

$ar^2 = 450$

Substitute the value of a , to solve for r;

$50r^2 = 450$

Divide both sides by 50 we get;

$r^2 = 9$

$r = \sqrt{9} = 3$

To find the term $a_2$;

$a_2 = ar$

Substitute the given values we have;

$a_2 = 50 \cdot 3 = 150$

Therefore, the possible value for the missing term of the geometric sequence is 150

Answer 2

For a geometric progression
a, b, c, d
there is a common ratio r equal to:
r = b/a = c/b = d/c

Let the missing number be x

r = x/50 = 450 /x
x² = 22500
x = 150