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Ksivusya [100]
3 years ago
8

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

Mathematics
1 answer:
denis-greek [22]3 years ago
3 0

Answer:

2^{n-3} is the nth term of the given sequence.

Step-by-step explanation:

The sequence given is

\frac{1}{4},\frac{1}{2},1,2,4 .....

We can clearly see that 1st term is \frac{1}{4} and 2nd term is \frac{1}{2}

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

2nd term is \frac{1}{2} 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 <em>Geometric Progression(GP)</em> with

First term, a = \frac{1}{4}

Common Ratio, r = 2

We know that n^{th} term for a GP is:

a_n = ar^{n-1}

Putting values of <em>a</em> and <em>r</em>

a_n = \dfrac{1}{4}2^{n-1}\\a_n = \dfrac{1}{2^{2} }2^{n-1}\\a_n = 2^{n-1-2}\\a_n = 2^{n-3}

Hence, 2^{n-3} is the nth term of the given sequence.

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