Question

question
find the 72nd term of the arithmetic sequence 11, 7, 3, ...
answer attempt 1 out of 2

Explanation:

Step1: Identify the first term and common difference

In an arithmetic sequence, the first term \(a_1\) is 11. The common difference \(d\) is found by subtracting consecutive terms: \(7 - 11=-4\), \(3 - 7 = - 4\), so \(d=-4\).

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 need to find the 72nd term, so \(n = 72\), \(a_1 = 11\), \(d=-4\).
Substitute the values into the formula: \(a_{72}=11+(72 - 1)\times(-4)\)

Step3: Calculate the value

First, calculate \(72-1 = 71\). Then, \(71\times(-4)=-284\). Then, \(11+(-284)=11 - 284=-273\).

Answer:

\(-273\)