#### Answer

a. $10661$
b. $10660$, underestimates by $1$ person.

#### Work Step by Step

a. Based on the given graph and numbers, we have
$\sum_{i=1}^5 a_i=a_1+a_2+a_3+a_4+a_5=1534+1781+932+2999+3415=10661$
which is the sum of the number of Americans who gave up their U.S. citizenship during 2010 to 2014.
b. Given
$a_n=498n+638$
we have
$a_1=498+638=1136, a_5=498(5)+638=3128$
Thus
$\sum_{i=1}^5 a_i=\frac{5(1136+3128)}{2}=10660$. Compare with the number from part-(a). It underestimates the actual sum by $1$ person.