Write the rule for the nth term of the following sequence.

1 over 4 comma 1 over 2 comma 1 comma 2 comma 4 comma ...

is the nth term of the given sequence.

Step-by-step explanation:

The sequence given is

We can clearly see that 1st term is and 2nd term is

2nd term is obtained by multiplying the 1st term by 2.

2nd term is and 3rd term is 1.

3rd term is obtained by multiplying the 2nd term by 2.

3rd term is 1 and 4th term is 2.

4th term is obtained by multiplying the 3rd term by 2.

Clearly, the given series is a Geometric Progression(GP) with

First term,

Common Ratio,

We know that term for a GP is:

Putting values of a and r

Hence, is the nth term of the given sequence.

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