# Chapter 10 - Section 10.2 - Arithmetic Sequences - Exercise Set - Page 1060: 65

a) $\$19,676$. b)$\$2$.

#### Work Step by Step

(a) The charges of public institutions which are given for the period of four years are 4565, 4824, 5046 and 5241 dollars. Thus, the total costs of the public dormitory charges will be: $\$4565+\$4824+\$5046+\$5241=\$19,676$. (b) Using the given model, we get,$\begin{align} & {{a}_{1}}=225\left( 1 \right)+4357 \\ & {{a}_{1}}=4582 \\ & {{a}_{4}}=225\left( 4 \right)+4357 \\ & {{a}_{4}}=5257 \end{align}$So,$\begin{align} & {{S}_{n}}=\frac{n}{2}\left( {{a}_{1}}+{{a}_{n}} \right) \\ & {{S}_{n}}=\frac{4}{2}\left( 4582+5257 \right) \\ & {{S}_{n}}=2\left( 9839 \right) \\ & {{S}_{n}}=\19,678\end{align} So, the model overestimates the actual sum by $19,678-19,676=\$2\$.

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.