Question

In the number series given below
6,28,120,496...​

Answer 1

6, 28, 120, 496, 2016

Step-by-step explanation:

This is a problem of mathematical reasoning of numbers and number series.

The first number = 6

The second number

= (6 * 4) + (4 * 2⁰)

= 24 + (4 * 1) = 24 + 4 = 28

The third number

= (28 * 4) + (4 * 2¹)

= 112 + (4 * 2) = 112 + 8 = 120

The fourth number

= (120 * 4) + (4 * 2²)

= 480 + (4 * 4) = 480 + 16 = 496

Using the above reasoning we can compute the next number as

= (496 * 4) + (4 * 2³)

= 1984 + (4 * 8) = 1984 + 32 = 2016

Thus solved.

• If we generalise a formula for the series, we can obtain a formula as follows,

X(n + 1) = {X(n) * 4} + (4 * 2ⁿ),

where n = 0, 1, 2, 3, ...

Some other reasoning problems to check out:

1. 42 21 22

78 ? 84

162 18 99

What is the number in question mark ?

- https://brainly.in/question/12789565

2. In the following number series which of the number will come in the place of missing place

6, 7, 17, 65, 323, ?

(a) 2415

(b) 1717

(c) 1937

(d) 2015

(e) None Of These

- https://brainly.in/question/12537795

Answer 2

The last number is $2016$

Step-by-step explanation:

Given,

The number series,

$6,28,120,496,?$  

1st number$=6$

2nd number,

$=(6\times 4)+(4\times 2^{0})$

$=24+4=28$

3rd number,

$=(28\times 4)+(4\times 2^{1})$

$=120$

4th number,

$=(120\times 4)+(4\times 2^{2})$

$=496$

5th number,

$=(496\times 4)+(4\times 2^{3})$

$=2016$

So, The last number is $2016$