Nont:Quetsion contain 5 parts each parts contain 5 marks and total marks of the whole question is 20

(i) 1, 8, 4, 27, 9,?

This series alternates between cubes and squares:

• $1 = 1^3$
• 8=2^3
• 4=2^2
• 27=3^3
• 9=3^2
• Next: 4^3=64

Missing number: 64

(ii) 3, 6, 8, 16, 18, ?

This series appears to follow a pattern:

• First, $3 to 6$ (adding 3)
• Then, $6 to 8$ (adding 2)
• Next, $8 to 16$ (doubling)
• Then, $16\to 18$ (adding 2)
• The next step likely doubles: $18 times 2 = 36$

Missing number: 36

(iii) 2, 8, 512, ?

This sequence involves raising the number to an increasing power of 3:

• $\mathrm{Cube\; Series}$
• $\mathrm{2\; x\; 2\; x\; 2\; =\; 8 \; (2^3=8)}$
• $\mathrm{8\; x\; 8\; x\; 8\; =\; 512\; (8^3\; =\; 512)}$
• $\mathrm{512\; x\; 512\; x\; 512\; =\; 134217728}$

(iv) 81, 9, 64, 8, ?, 12

This pattern alternates between division and taking the square root:

• $81÷9=9$
• $64 div 8 = 8$
• Next: $\sqrt{144}=12$

$\mathrm{<font\; color="\#ffffff"><b>(v)\; 6,\; 11,\; 21,\; 36,\; 56,\; ?</b></font>}$

Addition of Multiples of 5

6+5 =11

11 + 10 = 21

21 + 15 = 36

36 + 20 = 56

56 + 25 = 81