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What is the next number in the series 2, 1, $\frac{1}{2}$ ,...

What is the next number in the series 2, 1, $\frac{1}{2}$ , $\frac{1}{4}$ ...

A.

$\frac{1}{3}$

B.

$\frac{2}{8}$

C.

$\frac{3}{7}$

D.

$\frac{1}{8}$

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Correct answer is D

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

There are 4 terms in the series
Therefore the next number will be the 5th term

T_n = ar $^{n − 1}$ (formular for geometric series)

a = first term = 2

r = common rate = $\frac{\text{next term}}{\text{previous term}}$ = $\frac{1}{2}$

n = number of terms

T₅ = 5th term = ?

T₅ = ar $^{5 - 1}$

= ar $^4$

= 2 × (ar $^{n − 1}$ )⁴

= 2 × $\frac{1}{16}$

= $\frac{1}{8}$

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