Question

0, 6, 24, 60, 120, 210, ____.

Answer 1

Look at 1st difference sequence 6, 18, 36, 60, 90 __
Now look at the 2 nd difference sequence which is the difference sequence of the 1st difference sequence is 12, 18, 24, 30, ____
Is it now an arithmetic progression?
Don't forget what is an arithmetic progression and a geometric progression Revise the definitions one again
The required sequence was 0, 6, 24, 60, 120, 210, 336
Look at the question once again It may not be very obvious, but a better method to solve this question is
0=13−1,6=23−2,24=33−33−3,60=43−40=13−1,6=23−2,24=33−33−3,60=43−4
This given an answer 73−7=33673−7=336
The same as our previous result.