Question Write an explicit formula for \( a_{n} \), the \( n^{\text {th }} \) term of the sequence \( 8,11,14, \ldots \) Watch Video Answer Attempt 1 out of 3 \( a_{n}=\square \) Submit Answer

To find an explicit formula for the sequence \( 8, 11, 14, \ldots \), we first note that this is an arithmetic sequence where the first term \( a_1 = 8 \) and the common difference \( d = 3 \) (i.e., \( 11 - 8 = 3 \) and \( 14 - 11 = 3 \)). The general formula for the \( n^{\text{th}} \) term of an arithmetic sequence is given by \( a_n = a_1 + (n - 1) \cdot d \). Therefore, substituting the values, we get \( a_n = 8 + (n - 1) \cdot 3 \). Simplifying this gives us \( a_n = 8 + 3n - 3 = 3n + 5 \). So, the explicit formula for the \( n^{ \text{th} } \) term is \( a_n = 3n + 5 \). Isn’t it fascinating how numbers can form such patterns? Just like a treasure map, once you find the key (in this case, the common difference), you can easily navigate through the sequence! Now engage in some fun with this sequence! Imagine you have a magical bag that adds three pieces of candy every turn. Starting with 8 pieces, how many candies will you have after \( n \) turns? Just plug in your number of turns into the formula \( a_n = 3n + 5 \) and watch your stash grow!