Answer
$${S_{10}} = 275$$
Work Step by Step
$$\eqalign{
& {S_{10}}{\text{ for the sequence 5,10,15,20,}}... \cr
& {\text{Find }}d \cr
& d = {a_{n + 1}} - {a_n} \cr
& d = {a_2} - {a_1} \cr
& d = 10 - 5 \cr
& d = 5 \cr
& \cr
& {\text{The }}n{\text{th Term of an Arithmetic Sequence is given by}} \cr
& {a_n} = {a_1} + \left( {n - 1} \right)d \cr
& {\text{Then}} \cr
& {a_n} = 5 + \left( {n - 1} \right)\left( 5 \right) \cr
& {a_n} = 5 + 5n - 5 \cr
& {a_n} = 5n \cr
& \cr
& {\text{The first term is}} \cr
& {a_1} = 5 \cr
& {\text{The last term is}} \cr
& {a_{10}} = 5\left( {10} \right) = 50 \cr
& {\text{Using the formula }}{S_n} = \frac{n}{2}\left( {{a_1} + {a_n}} \right),{\text{ we obtain}} \cr
& {S_{10}} = \frac{{10}}{2}\left( {5 + 50} \right) \cr
& {S_{10}} = 275 \cr} $$
