Solve the following questions: 1. n2 + (n+1)2 + (n(n+1))2 = (n(n+1)+1)2. Fill in missing terms. 2. Sum of first n odd numbers. 3. Express a square number as sum of consecutive odd numbers.

Step 1: Solve Question 6. The given pattern is n^2 + (n+1)^2 + (n(n+1))^2 = (n(n+1)+1)^2. For 4^2 + 5^2 + \_ = 21^2: Here n=4. The missing term is (4 × 5)^2 = 20^2. The right side is (4 × 5 + 1)^2 = 21^2. So, 4^2 + 5^2 + 20^2 = 21^2. For 5^2 + \_ + 30^2 = 31^2: Here n=5. The second term is (n+1)^2 = (5+1)^2 = 6^2. The third term is (5 × 6)^2 = 30^2. The right side is (5 × 6 + 1)^2 = 31^2. So, 5^2 + 6^2 + 30^2 = 31^2. For 6^2 + 7^2 + \_ = \_ ^2: Here n=6. The third term is (6 × 7)^2 = 42^2. The right side is (6 × 7 + 1)^2 = 43^2. So, 6^2 + 7^2 + 42^2 = 43^2. Step 2: Solve Question 7. The sum of the first n odd numbers is n^2. (i)* 1+3+5+7+9 There are 5 odd numbers. 1+3+5+7+9 = 5^2 = 25 (ii)* 1+3+5+7+9+11+13+15+17+19 There are 10 odd numbers. 1+3+5+7+9+11+13+15+17+19 = 10^2 = 100 (iii)* 1+3+5+7+9+11+13+15+17+19+21+23 There are 12 odd numbers. 1+3+5+7+9+11+13+15+17+19+21+23 = 12^2 = 144 Step 3: Solve Question 8. The sum of the first n odd numbers is n^2. (i)* Express 49 as the sum of 7 odd numbers. Since 49 = 7^2, it is the sum of the first 7 odd numbers. 49 = 1+3+5+7+9+11+13 (ii)* Express 121 as the sum of 11 odd numbers. Since 121 = 11^2, it is the sum of the first 11 odd numbers. 121 = 1+3+5+7+9+11+13+15+17+19+21 Step 4: Solve Question 9. The number of non-square numbers between n^2 and (n+1)^2 is 2n. (i)* Between 12 and 13: Here n=12. Number of numbers = 2 × 12 = 24 (ii)* Between 25 and 26: Here n=25. Number of numbers = 2 × 25 = 50 (iii)* Between 99 and 100: Here n=99. Number of numbers = 2 × 99 = 198 Send me the next one 📸