Questions: In simplified form, write a formula for the nth term of the following arithmetic sequence: 35, 29, 23, 17, ... an = 6n + 41 an = -6n + 41 an = 6n + 35 an = -6n + 35

Transcript text: In simplified form, write a formula for the $n$th term of the following arithmetic sequence: $35,29,23,17, \ldots$ $a_{n}=6 n+41$ $a_{n}=-6 n+41$ $a_{n}=6 n+35$ $a_{n}=-6 n+35$

Solution

Solution Steps

Step 1: Identify the Common Difference

The given arithmetic sequence is $35, 29, 23, 17, \ldots$. To find the common difference $d$, subtract the second term from the first term:

\[ d = 29 - 35 = -6 \]

Step 2: Use the Formula for the $n$th Term of an Arithmetic Sequence

The formula for the $n$th term of an arithmetic sequence is:

\[ a_n = a_1 + (n-1) \cdot d \]

where $a_1$ is the first term and $d$ is the common difference.

Step 3: Substitute the Known Values

Substitute $a_1 = 35$ and $d = -6$ into the formula:

\[ a_n = 35 + (n-1)(-6) \]

Simplify the expression:

\[ a_n = 35 - 6n + 6 \]

Combine like terms:

\[ a_n = -6n + 41 \]

Final Answer

The formula for the $n$th term of the given arithmetic sequence is:

\[ \boxed{a_n = -6n + 41} \]

The answer is $a_n = -6n + 41$.

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