Question

NUMBER SERIES 136,55,28,19,16,?

Answer 1

Answer:

15

Step-by-step explanation:

given series is 136, 55 , 28 , 19 , 16 , ?

here the logic used is

136 - 55 = 81

55 - 28 = 27

28 - 19 = 9

19 - 16 = 3

so, we can observe that substraction of -3⁴, - 3³ , -3² , - 3¹

therefore, according to this next no which is to be added is -3⁰

hence, 16 - 3⁰ = 16 - 1 = 15 is the next series no.

so, 136,55,28,19,16,15

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Answer 2

Answer: The correct answer to the question is 15.

Step-by-step explanation:

The difference of a number in the series with its successor gives a geometric series whose common ratio is three. Now a Geometric series is defined as the sum of infinite numbers of certain terms that consists a constant ratio between two successive numbers.

For example:-

 $s_{n} =a+ar+ar^{2} +ar^{3} +ar^{4} +.....................+ar^{n\\} \\\\where\,\,\, a= first \,\,term\\\\r=common \,\,ratio$

In the given series the differences of each term from its successor gives a geometric series of 3 like-

$136-55=81=3^{4} \\55-28=27=\,\,3^{3} \\28-19=9=\,\,\,\,\,3^{2} \\19-16=3=\,\,\,\,\,3^{1} \,\,\,\,\\16-15=1=\,\,\,\,\,3^{0}$

$3^{0} +3^{1}+3^{2} +3^{3} +3^{4} +................+3^{n} \\\\\\where \,\,a=3^{0} =1\\\\r=\frac{3^{1} }{3^{0} } =\frac{3^{2} }{3^{1} } =\frac{3^{3} }{3^{2} } =3$

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