DIRECTIONS:
Find the next three terms of the sequence.
ANSWERS:
[tex] \blue {\overline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: }}[/tex]
[tex] \large \tt 11) \: 5,6,8,11,15,20,26,33[/tex]
[tex] 5 + \blue1 = 6 + \blue2 = 8 + \blue3 = 11 + \blue4 = 15 \\ 15+ \blue 5 = \boxed{20 }+ \blue6 = \boxed{ 26} + \blue 7 = \boxed{33}[/tex]
• The pattern tells us that we need to add a number that is increasing by one which also starts at one in getting the second term.
[tex] \blue {\overline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: }}[/tex]
[tex] \large \tt 12) \: 2,6,18,54,162,486,1458,4374[/tex]
[tex]2 \times \blue 3 = 6 \times \blue3 = 18 \times \blue3 = 54\times 3 = 162 \\ 162 \times \blue3 = \boxed{486} \times \blue 3 = \boxed{ 1458} \times \blue3 = \boxed{ 4374 }[/tex]
• The given sequence is a geometric one. We have a common ratio of 3, thus, a particular term must be multiplied by 3 to get the next term.
[tex] \blue {\overline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: }}[/tex]
[tex] \large \tt 13) \: 5,7,9,11,13,15,17,19[/tex]
[tex]5 + \blue2 = 7 + \blue2 = 9 + \blue2 = 11 + \blue2 = 13 \\ 13 + \blue2 = \boxed{ 15 }+ \blue2 = \boxed{17 }+ \blue2 = \boxed{19}[/tex]
• The given sequence is an arithmetic one. We have a common difference of 2, thus, a particular term must be added by 2 to get the next term.
[tex] \blue {\overline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: }}[/tex]
[tex] \large \tt 14) \: 4,9,16,25,36,49,64,81[/tex]
[tex] 2 {}^{2} = 4 \\ 3 {}^{2} = 9 \\ 4 {}^{2} = 16 \\ 5 {}^{2} = 25 \\ 6 {}^{2} = 36 \\ 7 {}^{2} = \boxed{ 49} \\ 8 {}^{2} = \boxed{64 }\\ 9 {}^{2} = \boxed{ 81}[/tex]
• The terms in the given sequence are perfect squares starting from 4.
[tex] \blue {\overline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: }}[/tex]
[tex] \large \tt 15) \: 5,25,125,625,3 125,15 \: 625,78 \: 125,390 \: 625[/tex]
[tex]5 \times \blue5 = 25 \times \blue5 = 125 \times \blue 5 = 625 \times \blue 5 = 3125 \\ 3125 \times \blue5 = \boxed{ 15625} \times \blue5 = \boxed{78125} \times \blue 5 = \boxed{ 390625}[/tex]
• The given sequence is a geometric one. We have a common ratio of 5, thus, a particular term must be multiplied by 5 to get the next term.
[tex] \blue {\overline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: }}[/tex]
