Answer:
Monday: 25
Tuesday: 121
Wednesday: 15
Step-by-step explanation:
Monday: square numbers
[tex] {1}^{2} = 1 [/tex]
[tex]2 {}^{2} = 4[/tex]
[tex] {3}^{2} = 9[/tex]
[tex] {4}^{2} = 16[/tex]
[tex] {5 }^{2} = 25[/tex]
[tex] {6}^{2} = 36[/tex]
Tuesday: add a power of 3
[tex] {3}^{1 } = 3[/tex]
[tex] {3}^{2} = 9[/tex]
[tex] {3}^{3} = 27 [/tex]
[tex] {3}^{4} = 81[/tex]
1+3=4, 4+9=13, 13+27=40, 40+81=121
Wednesday: one less than a power of 2
[tex] {2}^{1} - 1 = 2 - 1 = 1[/tex]
[tex] {2}^{2} - 1 = 4 - 1 = 3[/tex]
[tex] {2}^{3} - 1 = 8 - 1 = 7[/tex]
[tex] {2}^{4} - 1 = 16 - 1 = 15[/tex]
[tex] {2}^{5} - 1 = 32 - 1 = 31[/tex]
[tex] {2}^{6} - 1 = 64 - 1 = 63[/tex]
