\[
34,27,20,13, \ldots
\]

Write an explicit formula for the $n^{\text {th }}$ term $a_{n}$.

Answer

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Answer

So, the explicit formula for the nth term is $\boxed{a_n = 34 - 7(n - 1)}$.

Steps

Step 1 ：Given the sequence 34, 27, 20, 13, ...

Step 2 ：Notice that each term decreases by 7 from the previous term.

Step 3 ：This can be written as an arithmetic sequence with first term $a_1 = 34$ and common difference $d = -7$.

Step 4 ：The explicit formula for an arithmetic sequence is $a_n = a_1 + (n - 1) \cdot d$.

Step 5 ：Substitute $a_1 = 34$ and $d = -7$ into the formula.

Step 6 ：Simplify to get the final answer: $a_n = 34 - 7(n - 1)$.

Step 7 ：So, the explicit formula for the nth term is $\boxed{a_n = 34 - 7(n - 1)}$.