Question

find the 55th term of the arithmetic sequence 11, 21, 31, ...

Explanation:

Step1: Identify the formula for arithmetic sequence

The formula for the \(n\)-th term of an arithmetic sequence is \(a_n = a_1+(n - 1)d\), where \(a_1\) is the first term, \(d\) is the common difference, and \(n\) is the term number.

Step2: Find \(a_1\) and \(d\)

From the sequence \(11,21,31,\dots\), the first term \(a_1 = 11\). The common difference \(d=21 - 11=10\) (or \(31 - 21 = 10\)).

Step3: Calculate the 55th term

We need to find \(a_{55}\), so \(n = 55\), \(a_1=11\), \(d = 10\). Substitute into the formula:
\(a_{55}=11+(55 - 1)\times10\)
First, calculate \(55 - 1=54\). Then, \(54\times10 = 540\). Then, \(11+540 = 551\).

Answer:

\(551\)