Question

question
find the 53rd term of the arithmetic sequence 27, 11, -5, ...
answer attempt 1 out of 2
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Explanation:

Step1: Identify the first term and common difference

The first term \(a_1 = 27\). The common difference \(d\) is \(11 - 27=- 16\) (or \(-5 - 11=-16\)).

Step2: Use the arithmetic sequence formula

The formula for the \(n\)-th term of an arithmetic sequence is \(a_n=a_1+(n - 1)d\). For \(n = 53\), we substitute \(a_1 = 27\), \(d=-16\) and \(n = 53\) into the formula.
\(a_{53}=27+(53 - 1)\times(-16)\)

Step3: Calculate the value

First, calculate \(53 - 1 = 52\). Then, \(52\times(-16)=-832\). Then, \(a_{53}=27-832=-805\).

Answer:

\(-805\)