Question

Find the number next in the sequence:
6,24,60,120,?
Options are:
(a)180 (b)210 (c)240 (d)360

Answer 1

GIVEN :

The sequence is 6, 24, 60, 120,...

TO FIND :

The number next in the given sequence.

SOLUTION :

Given that the sequence is 6, 24, 60, 120,...

The first term 6 can be written as below

$0+1\times 6=6$

The second term 24 can be written as below

$6+3\times 6=24$

The third term 60 can be written as below

$24+6\times 6=60$

The fourth term 120 can be written as below

$60+10\times 6=120$

The next term fifth term can be written as

$120+15\times 6=210$

The differences between successive terms are , , , , ,... respectively.

They are of the form ,  where x=1, 3, 6, 10, 15,... respectively

i.e., x is of the series pattern 1, 1+2, 1+2+3, 1+2+3+4, 1+2+3+4+5,... respectively.

Option b) 210 is correct.

∴ the next term to the given sequence 6, 24, 60, 120,... is 210