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# find the following sum​

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Use​ Gauss's approach to find the following sum​ (do not use​ formulas):

4+9+14+19+...+59.

The sum of the sequence is

Guest Sep 21, 2017
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#1
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[59 - 4] / 5  + 1 =12 terms in the sequence

[59 + 4]  x  12/2 =

63   x         6     =378

Guest Sep 22, 2017
#2
+18629
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find the following sum

Use​ Gauss's approach to find the following sum​ (do not use​ formulas):

4+9+14+19+...+59.

The sum of the sequence is ?

$$\tiny{ \begin{array}{rcccccccccccccccccccccccc} && 4&+& 9&+&14&+&19&+&24&+&29&+&34&+&39&+&44&+&49&+&54&+&59 \\ &(reverse)& 59&+&54&+&49&+&44&+&39&+&34&+&29&+&24&+&19&+&14&+& 9&+& 4 \\ \hline &(sum)& 63&+&63&+&63&+&63&+&63&+&63&+&63&+&63&+&63&+&63&+&63&+&63 \\ \end{array} }$$

The sum of the sequence is $$\mathbf{\frac{ 12 * 63}{ 2}=378}$$

heureka  Sep 22, 2017

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