Number Line Sequences

Question

Fine the next three numbers in sequence.

 

1.  1,3,9,27, ....        2.    1,3,7,13, ...

Answer 1

1)  it looks as if the sequence consists of successive powers of 3; 81 is next (it's 3 times the predecessor term, 27).

2)  it appears as if each new number is increased by TWO plus the amount of the prior increase, i.e. from 1 to 3 is an increase of 2; from 3 to 7 is an increase of 4; from 7 to 13 is an increase of 6, so the next number must be 13 + 8.

 

For problems of this kind, you have to be creative, using your imagination, and use trial-and-error until something 'clicks.'