Question

Inductive Reasoning

A. 3, 5, 9, 12, 15, 18 ____,___,____,____,____

Answer 1

Hence, the nth term of the AP is a+(n-1)d

Where a is the first term and d is the common difference

In the above AP a=3 ,d =3

Therefore 7th term is 3+(7-1)3 = 3+6×3 = 3+18 = 21

Hence the next term is 21

Answer 2

(You will need to replace 5 into 6 , this is a correct option)

The difference between the numbers is 3.

So 6 is the 2nd term x by 3 = 6. 12 is the 4th term x by 3 is 12.

the 10th term would be, 10 x 3 = 30.

nth x by 3 = #(Result)

Conversely, 36/3 = 12. 36 is the 12th term., 27/3 = 9. 27 is the 9th term. etc.

Find the difference between the numbers in the sequence, then you will have your “key”, use that to work out the nth term.