Question

if $a_{18} = 12$ and $d = -3$, then $a_1 = ??$

Explanation:

Step1: Recall the arithmetic sequence formula

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

Step2: Substitute the given values into the formula

We know that \(a_{18}=12\), \(n = 18\), and \(d=-3\). Substituting these into the formula \(a_n=a_1+(n - 1)d\), we get \(12=a_1+(18 - 1)\times(-3)\).

Step3: Simplify the equation

First, calculate \((18 - 1)\times(-3)=17\times(-3)=- 51\). So the equation becomes \(12=a_1-51\).

Step4: Solve for \(a_1\)

To solve for \(a_1\), we add 51 to both sides of the equation: \(a_1=12 + 51\).

Step5: Calculate the value of \(a_1\)

\(12+51 = 63\).

Answer:

\(a_1 = 63\)