Notes

 

Questions

\(\textbf{1)}\) \(\displaystyle\sum_{i=1}^{5}3(2)^{i}\)

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The answer is \(186\)

 

\(\textbf{2)}\) \(a_1=3, \, r=5,\,\) solve for \(S_8\).

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The answer is \(S_8=292,968\)

 

\(\textbf{3)}\) \(a_1=3,\, a_5=48,\,\) solve for r and \(S_8\).

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The answer is \(r=2\) and \(S_8=765\)

 

\(\textbf{4)}\) \(r=\frac{1}{2},\, S_6=1,260,\,\) solve for \(a_1\).

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The answer is \(a_1=640\)

 

\(\textbf{5)}\) \(\frac{1}{9}+1+9+ \cdots +729\)

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The answer is \(820 \frac{1}{9}\,\) or \( \,\frac{7381}{9}\)

 

 

See Related Pages

\(\bullet\text{ Arithmetic Sequences}\)
\(\,\,\,\,\,\,\,a_n=a_1 + d(n-1)\)

\(\bullet\text{ Geometric Sequences}\)
\(\,\,\,\,\,\,\,a_n=a_1 \cdot r^{(n-1)}…\)

\(\bullet\text{ Arithmetic Series}\)
\(\,\,\,\,\,\,\,s_n=\frac{n}{2}(a_1+a_n)…\)

\(\bullet\text{ Infinite Geometric Series}\)
\(\,\,\,\,\,\,\,s_\infty = \frac{a_1}{1-r}\,\,\, |r| \lt 1…\)

\(\bullet\text{ Summation Notation}\)
\(\,\,\,\,\,\,\, \displaystyle \sum_{i=4}^{9} 3i-5 …\)

\(\bullet\text{ Recursive Sequences}\)
\(\,\,\,\,\,\,\, a_{1}=2, \, a_{n+1}=a_{n}+3…\)