Answer:
See Explanation
Step-by-step explanation:
Required
Complete the term and identify the rule
[tex](a)\ 5, 6, 8, [], 15[/tex]
We have:
[tex]5 + 1 = 6[/tex]
[tex]6 + 2 = 8[/tex]
[tex]8 + 3 = 11[/tex] --- Missing term
[tex]11 + 4 = 15[/tex]
The rule is:
Add current term to the position of term
i.e.
[tex]T_{n+1} = T_n + n[/tex]
[tex](b)\ 18, 20, 24, [], 38[/tex]
We have:
[tex]18 + 2*1 = 20[/tex]
[tex]20 + 2*2 = 24[/tex]
[tex]24 + 2 * 3 = 30[/tex] --- Missing term
[tex]30 + 2 * 4 = 38[/tex]
The rule is:
Add current term to twice the position of term
i.e.
[tex]T_{n+1} = T_n + 2 *n[/tex]
[tex](3)\ 14, 17, 20, 23, [][/tex]
We have:
[tex]14 + 3 = 17[/tex]
[tex]17 + 3 =20[/tex]
[tex]20 + 3 = 23[/tex]
[tex]23 + 3 = 26[/tex] --- Missing term
The rule is: Add 3
i.e.
[tex]T_{n+1} = T_n + 3[/tex]
[tex](4)\ 24, 30, 36, 42, [][/tex]
We have:
[tex]24 + 6 = 30[/tex]
[tex]30 + 6 = 36[/tex]
[tex]36 + 6 = 42[/tex]
[tex]42 + 6 = 48[/tex] --- Missing term
The rule is: Add 6
i.e.
[tex]T_{n+1} = T_n + 6[/tex]
[tex](5)\ 1, 10, 100[/tex]
We have:
[tex]10^0 = 1[/tex]
[tex]10^1 = 10[/tex]
[tex]10^2 = 100[/tex]
[tex]10^3 = 1000[/tex] -- Missing term
The rule is: 10 to the power of current position
i.e. [tex]T_n = 10^n[/tex]
