Answer :
Answer:
Therefore, the values are:
- \(a_5 = \frac{25}{7}\)
- \(a_6 = \frac{15}{4}\)
- \(a_7 = \frac{35}{9}\)
- \(a_{13} = \frac{13}{3}\)
Step-by-step explanation:
To find the sequence values \(a_5\), \(A_6\), \(A_7\), and \(a_{13}\) for the given expression \(a_n = \frac{5n}{n+2}\), we will calculate each value by substituting the appropriate \(n\) into the formula.
1. **\(a_5\):**
Substituting \(n = 5\):
\[
a_5 = \frac{5 \times 5}{5 + 2} = \frac{25}{7}
\]
2. **\(a_6\):**
Substituting \(n = 6\):
\[
a_6 = \frac{5 \times 6}{6 + 2} = \frac{30}{8} = \frac{15}{4}
\]
3. **\(a_7\):**
Substituting \(n = 7\):
\[
a_7 = \frac{5 \times 7}{7 + 2} = \frac{35}{9}
\]
4. **\(a_{13}\):**
Substituting \(n = 13\):
\[
a_{13} = \frac{5 \times 13}{13 + 2} = \frac{65}{15} = \frac{13}{3}
\]
Therefore, the values are:
- \(a_5 = \frac{25}{7}\)
- \(a_6 = \frac{15}{4}\)
- \(a_7 = \frac{35}{9}\)
- \(a_{13} = \frac{13}{3}\)
Good Luck
ans.
a5 = 3.57
a6 = 3.75
a7 = 3.89
a13 = 4.33
Step-by-step explanation:
Okay, let's solve this problem step-by-step.
Given the expression:
a = 5n / (n + 2)
We need to find the values of a for n = 5, 6, 7, and 13.
1. For n = 5:
a = 5(5) / (5 + 2)
a = 25 / 7
a5 = 3.57
2. For n = 6:
a = 5(6) / (6 + 2)
a = 30 / 8
a6 = 3.75
3. For n = 7:
a = 5(7) / (7 + 2)
a = 35 / 9
a7 = 3.89
4. For n = 13:
a = 5(13) / (13 + 2)
a = 65 / 15
a13 = 4.33
Therefore, the values are:
a5 = 3.57
a6 = 3.75
a7 = 3.89
a13 = 4.33