Complete the following number patterns and state the rule for each.

Here are the completed number patterns and their rules:

1) Copy and complete the number patterns:

• a) $1, 5, 9, \underline{13}, 17, \underline{21}, 25$

  • The pattern is to add 4 to the previous term.
  • $9+4=13$
  • $17+4=21$

• b) $3, 7, 11, 15, \underline{19}, \underline{23}, \underline{27}$

  • The pattern is to add 4 to the previous term.
  • $15+4=19$
  • $19+4=23$
  • $23+4=27$

• c) $1, 4, 9, 16, 25, \underline{36}, \underline{49}, \underline{64}$

  • The pattern is the sequence of perfect squares ($n^2$).
  • $1^2=1, 2^2=4, 3^2=9, 4^2=16, 5^2=25$
  • $6^2=36$
  • $7^2=49$
  • $8^2=64$

• d) $2, 4, 8, 16, 32, \underline{64}, \underline{128}, \underline{256}$

  • The pattern is to multiply the previous term by 2.
  • $32 \times 2=64$
  • $64 \times 2=128$
  • $128 \times 2=256$

2) Copy and complete, write down the rule:

• a) $9, 16, 25, \underline{36}, 49, \underline{64}, \underline{81}$

  • Rule = Square consecutive integers starting from 3.
  • $3^2=9, 4^2=16, 5^2=25$
  • $6^2=36$
  • $7^2=49$
  • $8^2=64$
  • $9^2=81$

• b) $21, 23, \underline{25}, \underline{27}, 29, \underline{31}, \underline{33}$

  • Rule = Add 2 to the previous term.
  • $23+2=25$
  • $25+2=27$
  • $29+2=31$
  • $31+2=33$