Question

Finding Terms of an Arithmetic Sequence Find the indicated term of the arithmetic sequence with the given description.

The $50\text{th}$ term is $1000$, and the common difference is $6$. Find the first and second terms.

Short answer

The first term is $706$ and the second term is $712$.

Step-by-step solution

Step 1. Given information.

The $50\text{th}$ term is $a_{50}=1000$.

The common difference is $d=6$.

Step 2. Write the concept.

The $n\text{th}$ term of an arithmetic sequence is:

$a_n=a+\left(n-1\right)d$

Where $a$ is the first term and $d$ is a common difference.

Step 3. Determine the first term.

The $50\text{th}$term is $a_{50}=1000$and the common difference is $d=6$.

$\begin{array}{c}a+\left(50-1\right)\left(6\right)=1000\\ a+\left(49\right)\left(6\right)=1000\\ a+294=1000\\ a=1000-294\\ a=706\end{array}$

Step 4. Determine the second term.

The second term of the sequence is:

$\begin{array}{c}{a}_2=a_1+d\\ =706+6\\ =712\end{array}$