What is the 50th term of the sequence that begins −4, 2, 8, 14, ...?

Solution:

The given sequence is −4, 2, 8, 14, ...

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

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

We know that a is the first term and d is the common difference.

Here, a = - 4 and d = 6

a_n = a+(n-1) d is the general term in an AP

For 50^th term, a₅₀ = a + (50 - 1) d

= - 4 + (50 - 1) × 6

= - 4 + 49 × 6

= - 4 + 294

= 290

Summary:

The 50th term of the sequence that begins -4, 2, 8, 14,... is 290.