Question

What is the 50th term of the sequence that begins −6, 0, 6, 12…?

Answer 1

The sequence is increasing by 6 each time, so to find the 50th term, we can use the formula for the nth term of an arithmetic sequence:

a_n = a_1 + (n-1)d

where:
a_n is the nth term
a_1 is the first term
d is the common difference between terms
n is the term number

Plugging in the values we have:
a_1 = -6
d = 6
n = 50

a_50 = -6 + (50-1)6
a_50 = -6 + 294
a_50 = 288

Therefore, the 50th term of the sequence is 288.