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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: $7,10,13,16,19, \ldots$
in Mathematics by Bronze Status (9,598 points) | 31 views

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Best answer

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:
$$
a_{100}=3(100)+4=304
$$

by Bronze Status (9,598 points)

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