Question

question
find the 52nd term of the arithmetic sequence -24, -7, 10, ...

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 \(d\)

Given the sequence \(-24, -7, 10, \dots\), \(a_1=-24\). The common difference \(d\) is calculated as \(d=-7 - (-24)=-7 + 24 = 17\).

Step3: Calculate the 52nd term

Substitute \(a_1=-24\), \(d = 17\), and \(n = 52\) into the formula:

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Answer:

\(843\)