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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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