Page 214 - Math Smart - 7

9.2.1 Simple number sequences

For each of the following sequences,
a) use a table to find a formula for the general term of the sequence.
b) find the 16*^ term, Tie-

O Multiples of three: 3, 6, 9, 12, 15,... in
@ Powers of four: 4, 16, 64, 256,... II
@ Perfect squares: 1,4, 9, 16, 25, ...
O Perfect cubes: 1, 8, 27, 64, 125, ...

Solution
O Multiples of three: 3, 6, 9, 12, 15, ...
a)
Position, n 1 2 3 4 5 ... n

1 X 3 2X3 3X3 4X3 5X3 « X 3
Term,
II
= 3 = 6 = 9 = 12 = 15 = 3/?
00
Hence, = 3n.
II
II
b) Tie = 3X16 = 48
@ Powers of four: 4, 16, 64, 256, ...
a)

Position, n 1 2 3 4 5 ... n
44
41 4^ 4^ 4/j
Term, Tp
= 4 = 16 = 256 = 1024
Hence, In = 4/i.
b) Tie = 4'^ = 4294 967 296

Q Perfect squares: 1, 4, 9, 16, 25, ...
a)
Position, n 1 2 3 4 5 ... n
,j2
V 2' 3^ 4^
Term, T^
1
= = 4 = 9 = 16
Hence, Tn = n^.
b) Tie = 16^ = 256
O Perfect cubes: 1, 8, 27, 64, 125, ...
a)
Position, n 1 2 3 4 5 ... n

1^ 43 5^ n'
Term, T^
= = 64 = 125
1
Hence, T^ =
b) Tie =16^ = 4096
210.) UNITS I Terms and Sequences