What is the 50th term of the sequence that begins with - 6, 0, 6, 12 ...

The 50th term is 288.

Step-by-step explanation:

A sequence that each term is related with the prior by a sum of a constant ratio is called a arithmetic progression, the sequence in this problem is one of those. In order to calculate the nth term of a setence like that we need to use the following formula:

an = a1 + (n-1) * r

Where an is the nth term, a1 is the first term, n is the position of the term in the sequence and r is the ratio between the numbers. In this case:

a50 = - 6 + (50 - 1) * 6

a50 = - 6 + 49*6

a50 = - 6 + 294

a50 = 288

The 50th term is 288.