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

`sum_51^100 7n`

The arithmetic sum formula is

`S_n=n/2(a_1+a_n)`

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

The first term in the sequence `a_1=7(51)=357.`

The last term in the sequence `a_n=7(100)=700`

`S_n=50/2(357+700)`

`S_n=25(1057)`

`S_n=26425`

`sum_51^100 7n`

The arithmetic sum formula is

`S_n=n/2(a_1+a_n)`

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

The first term in the sequence `a_1=7(51)=357.`

The last term in the sequence `a_n=7(100)=700`

`S_n=50/2(357+700)`

`S_n=25(1057)`

`S_n=26425`