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Find an equation for the general term of the given arithmetic sequence and use it to calculate its
$100^{\text {th }}$ term: $7,10,13,16,19, \ldots$
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Answer:

$a_{n}=3 n+4 ; a_{100}=304$

Explanation:

Begin by finding the common difference,
$$d=10-7=3$$
Note that the difference between any two successive terms is 3 . The sequence is indeed an
arithmetic progression where $a_{1}=7$ and $d=3$.
\begin{aligned} a_{n} &=a_{1}+(n-1) d \\ &=7+(n-1) \cdot 3 \\ &=7+3 n-3 \\ &=3 n+4 \end{aligned}
Therefore, we can write the general term $a_{n}=3 n+4$. Take a minute to verify that this equation
describes the given sequence. Use this equation to find the $100^{\text {th }}$ term:
$$a_{100}=3(100)+4=304$$

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