Question

Write a explicit formula for 5, 8, 11, 14, 17, 20…

Answer 1

The sequence you've provided is an arithmetic sequence where each term increases by 3. To find the explicit formula for this sequence, we can use the general formula for an arithmetic sequence:

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

where:
- \( a_n \) is the \( n \)-th term,
- \( a_1 \) is the first term (which is 5 in this case),
- \( d \) is the common difference (which is 3),
- \( n \) is the term number.

Plugging in the values:

- \( a_1 = 5 \)
- \( d = 3 \)

The explicit formula becomes:

\[ a_n = 5 + (n - 1) \cdot 3 \]
\[ a_n = 5 + 3n - 3 \]
\[ a_n = 3n + 2 \]

So the explicit formula for the sequence is:

\[ a_n = 3n + 2 \]