please help me!!!

Question

sandra wrote the sequence 3,6,11,18,27,...

what is the 12th term of this sequence?

Answer 1

You have

3, 6, 11, 18, 27 and can see that the difference to the previous values are as follow:

3, 5, 7, 9 (which is a sequence in itself of adding +2).

Knowing that, you can see that whatever formula for the sequence will have +2. If you subtract 2 to the current list of values you get:

1, 4, 9, 16, 25 which are all perfect squares so you can conclude that that n^2 + 2 will give you the original sequence.

Thus, the 12th term would be 12^2 + 2 = 144+2=146.

Answer 2

The pattern seems to be previous element +3, then +5, +7 +9 .....

So the 12th term would be

3 +3 +5 +7 +9 +11 +13 +15 +17 +19 +21 +23 (add all these)

Answer 3

the difference from the previous value is increasing by 2 every time so:

number value difference from previous value

1 3 0

2 6 3

3 11 5

4 18 7

5 27 9

6 38 11

7 51 13

8 66 15

9 83 17

10 102 19

11 123 21

12 146 23