Question

reasoning -number series 1,2,9,28,65,? ​

Answer 1

Subtract 1 from each term to get

2-1 = 1

9-1 = 8

28-1 = 27

65-1 = 64

Each number on the right hand side (RHS) is a perfect cube

1 = 1^3

8 = 2^3

27 = 3^3

64 = 4^3

So the rule is "cube the number, then add 1". We add 1 to undo the subtraction of 1 we did in the first part (see above)

So the rule is highlight%28n%5E3+%2B+1%29 where n is a positive whole number.

Once you get the general rule or formula, it's always a good idea to test it with the given sequence you already have. For instance, the third term is given to be 28. So if we did things right, then plugging n = 3 into the formula should give 28. Since n%5E3+%2B+1+=+3%5E3+%2B+1+=+27+%2B+1+=+28, this example confirms it. I recommend testing the other remaining terms.

The next term would be when n+=+5, so the next term is n%5E3+%2B+1+=+5%5E3+%2B+1+=+125+%2B+1+=+highlight%28126%29

Note: you can do each part in any order, but I find it easier to find the general rule/formula first



your answer is 126

Answer 2

it is geo-arithmetic progression

it is arithmetic and geometric progression

1st term=1

2nd term=

$(1) ^{3} + 1 = 2$

3rd term=

$(2) ^{3} + 1 = 9$

4th term=

$(3) ^{3} + 1 = 27 + 1 = 28$

5th term=

$(4) ^{3} + 1 = 64 + 1 = 65$

nth term=

$(n - 1) ^{3} + 1$
6th term=
(5)^3 +1=125+1=126