Question

question
find the 55th term of the arithmetic sequence 8, 24, 40, ...

answer attempt 1 out of 2

submit answer

Explanation:

Step1: Identify the first term and common difference

In an arithmetic sequence, the first term \(a_1 = 8\). The common difference \(d\) is found by subtracting the first term from the second term: \(d = 24 - 8 = 16\).

Step2: Use the arithmetic sequence formula

The formula for the \(n\)-th term of an arithmetic sequence is \(a_n = a_1 + (n - 1)d\). We want to find the 55th term, so \(n = 55\). Substitute the values: \(a_{55} = 8 + (55 - 1) \times 16\).

Step3: Calculate the 55th term

First, calculate \(55 - 1 = 54\). Then, \(54 \times 16 = 864\). Finally, \(a_{55} = 8 + 864 = 872\).

Answer:

872