Question

note: please make sure to properly format your answers. all dollar figures in the answers need to include the dollar sign and any amount over 1,000 should include comma ($2,354.67). all percentage values in the answers need to include a percentage sign (%). for all items without specific rounding instructions, round your answer to two decimal places, show both decimal places (5.06). a finite arithmetic sequence has 12 terms. the last term is 100 and the common difference is 3. what is the first term?

Explanation:

Step1: Recall 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 number of terms, and $d$ is the common difference.

Step2: Identify given values

We know that $n = 12$, $a_{12}=100$, and $d = 3$.

Step3: Substitute values into formula

Substitute into $a_n=a_1+(n - 1)d$: $100=a_1+(12 - 1)\times3$.

Step4: Simplify the equation

First, calculate $(12 - 1)\times3=11\times3 = 33$. So the equation becomes $100=a_1 + 33$.

Step5: Solve for $a_1$

Subtract 33 from both sides of the equation: $a_1=100 - 33$.
$a_1 = 67$

Answer:

67