Find the 50th term of the sequence 5, -2, -9, -16

Solution:

Given sequence:

5 - 2 - 9 - 16

Common difference is -2 - 5 = -7

First term is 5

An arithmetic progression (AP) is a sequence where the differences between every two consecutive terms are the same.

In an arithmetic progression, there is a possibility to derive a formula for the nth term of the AP.

From arithmetic progression,

we have a_n = a + d(n - 1)

a₅₀ = 5 - 7(50 - 1)

= -338

Therefore, the 50th term is -338.

Find the 50th term of the sequence 5, -2, -9, -16

Summary:

The 50th term of the sequence 5 ,-2, -9, -16 is -338.