Question

write an expression to describe the sequence below, and then find the 50th term. use n to represent the position of a term in the sequence, where n = 1 for the first term. -31, -30, -29, -28, ... a_n = a_50 =

Explanation:

Step1: Identify sequence type

This is an arithmetic sequence with first term \(a_1 = -31\) and common difference \(d = 1\) (since \(-30 - (-31) = 1\), \(-29 - (-30) = 1\), etc.).

Step2: Arithmetic sequence formula

The formula for the \(n\)-th term of an arithmetic sequence is \(a_n = a_1 + (n - 1)d\). Substituting \(a_1 = -31\) and \(d = 1\), we get:
\(a_n = -31 + (n - 1)(1)\)
Simplify: \(a_n = -31 + n - 1 = n - 32\)

Step3: Find the 50th term

Substitute \(n = 50\) into \(a_n = n - 32\):
\(a_{50} = 50 - 32 = 18\)

Answer:

\(a_n = n - 32\)
\(a_{50} = 18\)