Question

A sequence of numbers begins with 12 and progresses geometrically. each number is the previous number divided by 2. which value can be used as the common ratio in an explicit formula that represents the sequence?

Answer 1

1/2 value can be used as the common ratio in an explicit formula that represents the sequence.

Definition of sequence -

• The following of one thing after another; succession. order of succession: a list of books in alphabetical sequence.
• A continuous or connected series: a sonnet sequence. something that follows; a subsequent event; result; consequence.

A sequence that progresses geometrically has the first term as 12.

Each number is the previous number divided by 2.

so the sequence will be 12, 6, 3, 1.5...........

Explicit formula of a geometric sequence is given by

$T_{n} = ar^{n-1}$

Where $T_{n}$  = nth term of the sequence

a = first term

r = common ratio

and n = number of term

In this sequence common ratio = $\frac{Successive term }{previous term}$

            = 6/12

            =  1/2

Therefore, common ratio will be 1/2.

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