How does the total number of molecules increase as the terms progress?
a_n=3n
There are 69 atoms in 23 molecules.
Practice makes perfect
If there is one water molecule, there are two hydrogen H and one oxygen O atoms. For two molecules, there are four H atoms and two O atoms. If we add one more water molecule, there will be six H atoms and three O atoms. This pattern will continue on in this way. Let's illustrate this pattern in a table.
Number of hydrogen atoms
1
2
3
4
Number of oxygen atoms
2
4
6
8
Total number of atoms
3
6
9
12
In the third row, the total number of atoms form an arithmetic sequence:
3,6,9,12,...
where the first term is 3 and we find the next term by adding the common difference 3 to its preceding term. We can use the formula for an arithmetic sequence to find the number of atoms in 23 molecules.
