Write an expression for the arithmetic sequence whose 2 nd term is 8 and whose 5 th term is 17

Ask by Cole Floyd. in Japan

Jan 24,2025

Question

Write an expression for the arithmetic sequence whose 2 nd term is 8 and whose 5 th term is 17 $$ a_{n}=17-3 n $$ $$ a_{n}=8+3 n $$ $$ a_{n}=3 n+2 $$ $$ a_{n}=3 n+5 $$

UpStudy AI · Accepted Answer

To find the arithmetic sequence where the 2nd term is 8 and the 5th term is 17, let's use the general formula for an arithmetic sequence:

$$ a_n = a + (n-1)d $$

where:
- $$ a $$ is the first term,
- $$ d $$ is the common difference,
- $$ n $$ is the term number.

**Given:**
1. The 2nd term ($$ a_2 $$) is 8:
   $$ a + d = 8 $$
2. The 5th term ($$ a_5 $$) is 17:
   $$ a + 4d = 17 $$

**Steps to Solve:**

1. **Subtract the first equation from the second to eliminate $$ a $$:**
   $$
   (a + 4d) - (a + d) = 17 - 8 \
   3d = 9 \
   d = 3
   $$

2. **Find the first term ($$ a $$) using $$ d = 3 $$ in the first equation:**
   $$
   a + 3 = 8 \
   a = 5
   $$

3. **Write the general formula for the sequence:**
   $$
   a_n = a + (n-1)d \
   a_n = 5 + (n-1) \times 3 \
   a_n = 5 + 3n - 3 \
   a_n = 3n + 2
   $$

**Therefore, the arithmetic sequence is:**
$$ a_{n} = 3n + 2 $$

**Answer:**  
$$ a_{n}=3 n+2 $$
The arithmetic sequence is $$ a_{n} = 3n + 2 $$.

Write an expression for the arithmetic sequence whose 2 nd term is 8 and whose 5 th term is 17

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