number 7 **Mathematics Series and Sequences**---**Exercises:****6. Find the sum of the series \(A = 5, 3, 1, \ldots, -11\).**- To find the sum of this arithmetic series, you need to determine the first term (\(a\)), the common difference (\(d\)), the last term (\(l\)), and the number of terms (\(n\)).- Formula for the sum of an arithmetic series: \(S_n = \frac{n}{2} (a + l)\).**7. Find the sum of the initial six terms of \(\{2, 5, \ldots\}\) if...** a. **...It is an arithmetic series.** - For an arithmetic series, the common difference (\(d\)) can be found by subtracting the first term from the second term. - Use the sum formula for the first six terms (\(S_n = \frac{n}{2} (2a + (n-1)d)\)). b. **...It is a geometric series.** - For a geometric series, you need to find the common ratio (\(r\)). - Use the sum formula for the first six terms of a geometric series (\(S_n = a \frac{1-r^n}{1-r}\)).---**8. Is \(200 + 198 + 196 + 194 + \ldots\) a convergent or divergent series? Explain.**---**Section III**In this section, we explore the convergence and divergence of series and sequences. You will apply tests and concepts to determine whether given series converge or diverge based on their terms and behavior at infinity.

Name: number 7 **Mathematics Series and Sequences**---**Exercises:****6. Fin
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Description: number 7 **Mathematics Series and Sequences**---**Exercises:****6. Find the sum of the series \(A = 5, 3, 1, \ldots, -11\).**- To find the sum of this arithmetic series, you need to determine the first term (\(a\)), the common difference (\(d\)), the