Question

find the reasoning :-
6,6,7,8,12,16​

Answer 1

Step-by-step explanation:

we have to find the differences between the numbers sequentially .

6-6=0

7-6=1

8-7=1

12-8=4

16-12=4

So I think next differences are 9, 9 because once we observe the differences the gap between them are 1 , 3 (odd no.) , next one will be 5 so we have to Add the five to 4 ,4 it will be 9 , 9 .

so finally I think this the reasoning between them..

Answer 2

answer: The correct answer is 21. I see a lot of people got that answer entirely by mistake. Let me explain.

4,5,6,7,9,12,16,21 is the collection of all elements of a discrete natural number sequence known as Dwight’s Sequence. (you may not have heard of it)

The elements of the sequence are defined as that sequence of numbers generated by two alternating formulas:

x×y

2(x-1)-1+x×y

x and y start with values of 1 each. With each completed cycle of the formulas, the y value is incremented by 1 if it’s equal to x. Otherwise, the x value is incremented. The sequence begins at the first value that is higher than the previously generated value and that is followed by a value higher than itself. The sequence ends at the value that precedes a lesser value. If the same value is generated twice, the value is discarded, the increment procedure is repeated, and the alternation cycles back to the first step. (this rule may seem arbitrary, but I assure you it isn’t)

1×1=1

2(1-1)-1+1×1=0

1×2=2

2(1-1)-1+1×2=1

2×2=4

2(2-1)-1+2×2=5

2×3=6

2(2-1)-1+2×3=7

3×3=9

2(3-1)-1+3×3=12

3×4=12 (repeat value; discard and increment; cycle to formula 1)

4×4=16

2(4-1)-1+4×4=21

4×5=20

As you can see by my helpful use of italics, the entire sequence is 4,5,6,7,9,12,16,21. Whoever asked the question cleverly obscured the 4 and 5, misleading many good Quorans into thinking they were looking at a simpler, far less useful sequence.

As you can see, this sequence has many math applications and logic, and it is elegant as all get-out.

Step-by-step explanation:

Mark me brainlist please