Question Write an explicit formula for $$ a_{n} $$, the $$ n^{ ext {th }} $$ term of the sequence $$ 30,35,40, \ldots $$ Answer Attempt 1 out of 3 $$ a_{n}=\square $$ Submit Answer

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Question Write an explicit formula for $$ a_{n} $$, the $$ n^{	ext {th }} $$ term of the sequence $$ 30,35,40, \ldots $$ Answer Attempt 1 out of 3 $$ a_{n}=\square $$ Submit Answer

UpStudy AI · Accepted Answer

To find the explicit formula for the $$ n^{\text{th}} $$ term of the sequence $$ 30, 35, 40, \ldots $$, we first need to identify the pattern in the sequence.

1. **Identify the first term and the common difference:**
   - The first term $$ a_1 = 30 $$.
   - The second term $$ a_2 = 35 $$.
   - The third term $$ a_3 = 40 $$.

The common difference $$ d $$ can be calculated as:
   $$
   d = a_2 - a_1 = 35 - 30 = 5
   $$
   $$
   d = a_3 - a_2 = 40 - 35 = 5
   $$

2. **General formula for an arithmetic sequence:**
   The general formula for the $$ n^{\text{th}} $$ term of an arithmetic sequence is given by:
   $$
   a_n = a_1 + (n - 1) \cdot d
   $$

3. **Substituting the known values:**
   Now, substituting $$ a_1 = 30 $$ and $$ d = 5 $$ into the formula:
   $$
   a_n = 30 + (n - 1) \cdot 5
   $$

4. **Simplifying the formula:**
   $$
   a_n = 30 + 5n - 5
   $$
   $$
   a_n = 5n + 25
   $$

Thus, the explicit formula for the $$ n^{\text{th}} $$ term of the sequence is:
$$
a_n = 5n + 25
$$

You can now submit this answer.
The explicit formula for the $$ n^{\text{th}} $$ term is $$ a_n = 5n + 25 $$.

Question Write an explicit formula for \( a_{n} \), the \( n^{\text {th }} \) term of the sequence \( 30,35,40, \ldots \) Answer Attempt 1 out of 3 \( a_{n}=\square \) Submit Answer

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