Question

What is the next number in the series.....0, 6, 24, 60, 120, 210, ?

Answer 1

0=1-1

=1^3-1

6=8-2

=2^3-2

24=27-3

=3^3-3

60=64-4

=4^3-4

120=125-5

=5^3-5

210=216-6

=6^3-6

according to this logic the next term should be

7^3-7

=343-7

=336

so your required answer is 336

Answer 2

Answer:

The next number in the given A.P is0, 6, 24, 60, 120, 210, 336.

Step-by-step explanation:

An arithmetic progression or arithmetic sequence is a series of numbers such that the difference between the consecutive terms exists constant.

• If the same number exists added or subtracted from each term of an A.P, then the resultant terms in the sequence exist also in A.P with the exact common difference.
• If each term in an A.P exists divided or multiply with the identical non-zero number, then the consequent sequence is also in an A.P.

The next term in the A.P is 336.

It is proved from the following calculation.

$&2^{3}-2=6$

$&3^{3}-3=24$

$&4^{3}-4=60$

$&5^{3}-5=120$

$&6^{3}-6=210$

$&7^{3}-7=336$

Therefore, The next number in the given A.P is0, 6, 24, 60, 120, 210, 336.

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