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for (U sub n) Un=3n-1, list U1+U2+U3+....+U20 and find its sum

 Sep 22, 2014

Best Answer 

 #1
avatar+26400 
+5

for (U sub n) Un=3n-1, list U1+U2+U3+....+U20 and find its sum

$$U_n=3n-1\\ \\
\begin{array}{|c|c|}
\hline
n & U_n \\
\hline
1 & 2 \\
2 & 5 \\
3 & 8 \\
4 & 11 \\
5 & 14 \\
6 & 17 \\
7 & 20 \\
8 & 23 \\
9 & 26 \\
10 & 29 \\
11 & 32 \\
12 & 35 \\
13 & 38 \\
14 & 41 \\
15 & 44 \\
16 & 47 \\
17 & 50 \\
18 & 53 \\
19 & 56 \\
20 & 59 \\
\hline
\end{array}$$

sum:

$$\begin{array} {*{20}{c}}
&
2
&+&
5
&+&
8
&+&
11
&+&
14
&...&
47
&+&
50
&+&
53
&+&
56
&+&
59
\\
&
59
&+&
56
&+&
53
&+&
50
&+&
47
&...&
14
&+&
11
&+&
8
&+&
5
&+&
2
\\
\hline
sum
&
61
&+&
61
&+&
61
&+&
61
&+&
61
&...&
61
&+&
61
&+&
61
&+&
61
&+&
61
\end{array}
\\ \\
sum = \frac{1}{2}*20 * 61 = 610$$

 Sep 22, 2014
 #1
avatar+26400 
+5
Best Answer

for (U sub n) Un=3n-1, list U1+U2+U3+....+U20 and find its sum

$$U_n=3n-1\\ \\
\begin{array}{|c|c|}
\hline
n & U_n \\
\hline
1 & 2 \\
2 & 5 \\
3 & 8 \\
4 & 11 \\
5 & 14 \\
6 & 17 \\
7 & 20 \\
8 & 23 \\
9 & 26 \\
10 & 29 \\
11 & 32 \\
12 & 35 \\
13 & 38 \\
14 & 41 \\
15 & 44 \\
16 & 47 \\
17 & 50 \\
18 & 53 \\
19 & 56 \\
20 & 59 \\
\hline
\end{array}$$

sum:

$$\begin{array} {*{20}{c}}
&
2
&+&
5
&+&
8
&+&
11
&+&
14
&...&
47
&+&
50
&+&
53
&+&
56
&+&
59
\\
&
59
&+&
56
&+&
53
&+&
50
&+&
47
&...&
14
&+&
11
&+&
8
&+&
5
&+&
2
\\
\hline
sum
&
61
&+&
61
&+&
61
&+&
61
&+&
61
&...&
61
&+&
61
&+&
61
&+&
61
&+&
61
\end{array}
\\ \\
sum = \frac{1}{2}*20 * 61 = 610$$

heureka Sep 22, 2014

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