**Finding the First Four Terms and the 10th Term of a Sequence**For the sequence defined by the formula \( a_n = \frac{(-1)^n}{5n} \), we are asked to determine the first four terms and the 10th term.### Sequence Definition:\[ a_n = \frac{(-1)^n}{5n} \]### Calculating the Terms:1. **First Term \((n = 1)\)**:\[ a_1 = \frac{(-1)^1}{5 \cdot 1} = \frac{-1}{5} = -0.2 \]2. **Second Term \((n = 2)\)**:\[ a_2 = \frac{(-1)^2}{5 \cdot 2} = \frac{1}{10} = 0.1 \]3. **Third Term \((n = 3)\)**:\[ a_3 = \frac{(-1)^3}{5 \cdot 3} = \frac{-1}{15} \approx -0.0667 \]4. **Fourth Term \((n = 4)\)**:\[ a_4 = \frac{(-1)^4}{5 \cdot 4} = \frac{1}{20} = 0.05 \]5. **10th Term \((n = 10)\)**:\[ a_{10} = \frac{(-1)^{10}}{5 \cdot 10} = \frac{1}{50} = 0.02 \]### Terms Summary:- First Term (\(a_1\)): \(-0.2\)- Second Term (\(a_2\)): \(0.1\)- Third Term (\(a_3\)): \(-0.0667\)- Fourth Term (\(a_4\)): \(0.05\)- 10th Term (\(a_{10}\)): \(0.02\)### ExplanationThe values alternate signs because the numerator, \((-1)^n\), switches between \(-1\) and \(1\) depending on whether \(n\) is odd or even. The denominator involves the product of \(5\) and \(n\), causing the values to decrease as \(n\) increases since the denominator is getting larger.---This

Name: **Finding the First Four Terms and the 10th Term of a Sequence**For t
Uploaded: 2024-03-20T06:38:58.000Z
Channel: Bartleby
Description: **Finding the First Four Terms and the 10th Term of a Sequence**For the sequence defined by the formula \( a_n = \frac{(-1)^n}{5n} \), we are asked to determine the first four terms and the 10th term.### Sequence Definition:\[ a_n = \frac{(-1)^n}{5n