I see the pattern 7,8,9

Then I see the pattern 16, 27 so that's 8*2 then 9*3

Next number could be 10*4 = 40

This is one possible answer that's logical.

But there are other answers too.

OR

16 + 11 = 27

so 27 + 11 = 38 so the next number is 38

OR

16 = 4^2

27 = 3^3

so then 2^4 = 16 so the next number is 16

OR

y = -(9 x^4)/2 + (157 x^3)/3 - 210 x^2 + (2041 x)/6 - 171 also works

so -219 so the next number is -219

There are probably an infinite number of answers unless you place more restrictions on the problem.

7,16,8,27,9,40,10

8 x 2 = 16

9 x 3 = 27

10 x 4 = 40

These are easier than most people think. The next term is always zero.

nth term = 1/60(109n⁵ - 1905n⁴ + 12405n³ - 37125n² + 50276n - 23340)

6th term = 1/60[109(6)⁵ - 1905(6)⁴ + 12405(6)³ - 37125(6)² + 50276(6) - 23340] = 0

7, 16, 8, 27, 9

Next in sequence is 38.

I would suggest 40.

An answer of 38 looks more like numerology.

Cheers!

7, 8*2, 8, 9*3, 9

Next is 10*4 = 40

To get 38, do differences

+9, -8, +19, -18, +29

Instead of +29, it could be +39 (twice +19 +1), which makes the next number 48

Since 7,8,9 form an obvious arithmetic sequence, it might be reasonable to make a simple arithmetic sequence that starts with 16, 27, and then (?)...which would be 38.

But I still say your teacher is an imbecile. There is no single "right" answer to a question like this one. You are simply being asked to guess what pattern your teacher has in mind. Shame on him! (or her.)

40

7x2=14+2= 16

8x3=24+3= 27

9x4=36+4= 40

38

7, 8, and 9 are in sequential order. 16 + 11= 27 so 27 + 11= 38.

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