Answer
$S_{4}=1500$ bacteria
Work Step by Step
$a_{n}=100\cdot2^{n-1}$ defines the sequence, where $n$ is the number of $6$-hour periods.
In the first $24$ hours, $4$ $6$-hour periods passed, so the number of bacteria is obtained by:
$a_{1}=100\cdot2^{1-1}=100\cdot2^{0}=100\cdot1=100$
$a_{2}=100\cdot2^{2-1}=100\cdot2^{1}=100\cdot2=200$
$a_{3}=100\cdot2^{3-1}=100\cdot2^{2}=100\cdot4=400$
$a_{4}=100\cdot2^{4-1}=100\cdot2^{3}=100\cdot8=800$
$S_{4}=a_{1}+a_{2}+a_{3}+a_{4}$
$S_{4}=100+200+400+800=1500$
