Question

1/3+2/3+(-1/21)+4/9​

Answer 1

Answer:

believe the sequence is as follows..

2,1=9 (2×4)+1=9

*3,2=14 (3×4)+2=14 }5

4,2=18 (4×4)+2=18 }4

*5,3=23 (5×4)+3=23 }5

6,3=27 (6×4)+3=27 }4

*7,4=32 (7×4)+4=32 }5

*8,4=36 (8×4)+4=36 }4

*9,4=40 (9×4)+4=40 }4

*10,5=45 (10×4)+5=45 }5

I followed the sequence and figured that the number 4 is the only number that each can be multiplied by to achieve the equal to amount associated with each pairing after adding the second number in each coupling. So it would look like solving for x.

Ex. 3,4=16 3x+4=16 16–4=12 12÷3=4 x=4

But the coupling 5,3=18 would then be incorrect because:(5×4)+3=23

So for the sequence to work, the 5,3=18 would have to be changed to 5,3=23 in which it now fits and works to solve for x which is 4. There was a pattern of the numbers 4 and 5 that surfaced as the difference between each pairings sum total. The difference between each sum was alternating between the numbers 4 and 5, which equal 9 when added together. Which also helped me to form a chart of sorts that makes sense. My answer is typed above, that is the most stable conclusion that I could come to to make sense of the pairings that were listed.

Answer 2

Answer:

....

Step-by-step explanation:

$\frac{1}{3 } + \frac{2}{3} + ( - \frac{1}{21} ) + \frac{4}{9} \\ \frac{1}{3} + \frac{2}{3} - \frac{1}{21} + \frac{4}{9} \\ \frac{21 + 42 - 3 + 28}{63} \\ \frac{91 - 3}{63} \\ \frac{88}{63}$