Special Pattern 01

Q. Find the missing number using the given pattern.
$2^2+3^2+6^2=7^2{3}^2+4^2+{12}^2={13}^2{4}^2+5^2+({)}^2=({)}^2$

1. 15, 16
2. 20, 21
3. 25, 24
4. 24, 23

Q. Without adding, find the sum of the following numbers
(i) 1 + 3 + 5 + 7 + 9 =
(ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 =
(iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25 =
[3 marks]

Q. Fill in the blanks.
$5^2+6^2+({)}^2=(31{)}^2$

1. 30
2. 31
3. 29
4. 20

Q. $\text{If}{11}^2=121,{101}^2=10201\text{find the square of 1001.}$

1. 100001
2. 1002001
3. 10021
4. 1002

Q. Fill in the blanks.
$6^2+7^2+{42}^2=({)}^2$

1. 43
2. 45
3. 40
4. 41

Q. $(1965{)}^2$ = ?

1. 3961254

2. 3861286

3. 3562341

4. 3861225

Q. Match the following with their equivalents.

1. 1+3+5+7+9+11+13
2. 12+13
3. $5\times 7$
4. 6+10

Q. Find the missing number using the given pattern.
$2^2+3^2+6^2=7^2{3}^2+4^2+{12}^2={13}^2{4}^2+5^2+{20}^2={21}^2$
What is the general form for the above pattern?

1. $(m{)}^2+(m+1{)}^2+\left(\right(m)\times (m+1){)}^2=(\left(m\right)\times (m+1)+1{)}^2$
   
   
2. $(m{)}^2+(m+1{)}^2+\left(\right(m)\times (m+1){)}^2=(\left(m\right)\times (m+1){)}^2$
   
3. $(m{)}^2+(m+1{)}^2+\left(\right(m)\times (m){)}^2=(\left(m\right)\times (m+1)+1{)}^2$
   
4. $(m{)}^2+(m{)}^2+\left(\right(m)\times (m+1){)}^2=(\left(m\right)\times (m+1)+1{)}^2$
   

Q. Tap on the triangular numbers among the following.

1. 1
2. 2
3. 3
4. 6
5. 9
6. 10
7. 16
8. 28

Q.

$\text{Find the value of}(66666{)}^2.$

1. 222237776

2. 4444355556

3. 4444655556

4. 445544554455