Question

Find the 11th partial sum of the summation of negative 7i plus 22, from i equals 1 to infinity.

Answer 1

I think you mean,

$\sum_{i=1}^{\infty}(7i+22)$

You can use the usual formula,

$S_{k}=\frac{k}{2}(a_1+a_k)$

That in this case is,

$S_{11}=\frac{11}{2}(29+99)=704$

Where I have used,

$a_k=7\cdot k +22$