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

Solution:

An arithmetic progression is a sequence in which the difference between a pair of consecutive numbers is equal.

The given sequence is -6, 0, 6, 12, ...

It is in arithmetic progression as the common difference between all consecutive numbers is 6.

Let a₁ be the first term and d be the common difference.

Therefore, a₁ = - 6 and d = 6

For 50^th term, a₅₀ = a₁ + (n - 1) d

= - 6 + (50 - 1) 6

= - 6 + 49 × 6

= - 6 + 294

= 288

Thus, the 50^th term of the sequence is 288.

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

Summary:

The 50^th term of the sequence that begins with - 6 is 288.