Notes: `sum_(n=51)^100 (7n)` Find the partial sum.

Saturday, April 29, 2017

$\displaystyle{\sum_{{{n}={51}}}^{{100}}}{\left({7}{n}\right)}$ Find the partial sum.

$\displaystyle{\sum_{{51}}^{{100}}}{7}{n}$

The arithmetic sum formula is

$\displaystyle{S}_{{n}}=\frac{{n}}{{2}}{\left({a}_{{1}}+{a}_{{n}}\right)}$

The number of terms in the sequence is n=50.

The first term in the sequence $\displaystyle{a}_{{1}}={7}{\left({51}\right)}={357}.$

The last term in the sequence $\displaystyle{a}_{{n}}={7}{\left({100}\right)}={700}$

$\displaystyle{S}_{{n}}=\frac{{50}}{{2}}{\left({357}+{700}\right)}$

$\displaystyle{S}_{{n}}={25}{\left({1057}\right)}$

$\displaystyle{S}_{{n}}={26425}$

$\displaystyle{\sum_{{51}}^{{100}}}{7}{n}$

The arithmetic sum formula is

$\displaystyle{S}_{{n}}=\frac{{n}}{{2}}{\left({a}_{{1}}+{a}_{{n}}\right)}$

The number of terms in the sequence is n=50.

The first term in the sequence $\displaystyle{a}_{{1}}={7}{\left({51}\right)}={357}.$

The last term in the sequence $\displaystyle{a}_{{n}}={7}{\left({100}\right)}={700}$

$\displaystyle{S}_{{n}}=\frac{{50}}{{2}}{\left({357}+{700}\right)}$

$\displaystyle{S}_{{n}}={25}{\left({1057}\right)}$

$\displaystyle{S}_{{n}}={26425}$

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