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# Without adding, find the sum.

(i) 1 + 3 + 5 + 7 + 9

(ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 +19

(iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23

**Solution:**

Sum of Consecutive odd numbers is given.

We know that, sum of the first n odd natural numbers is n^{2}

(i) 1 + 3 + 5 + 7 + 9

Here number of term (n) is 5

Sum = (5)^{2} = 25

(ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19

Here number of term (n) is 10

Sum = (10)^{2} = 100

(iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23

Here number of term (n) is 12

Sum = (12)^{2} = 144

**☛ Check: **NCERT Solutions for Class 8 Maths Chapter 6

**Video Solution:**

## Without adding, find the sum. (i) 1 + 3 + 5 + 7 + 9 (ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 +19 (iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23

NCERT Solutions for Class 8 Maths Chapter 6 Exercise 6.1 Question 7

**Summary:**

Without adding, the sum of the following (i) 1 + 3 + 5 + 7 + 9 (ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 +19 (iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 are (i) 25, (ii) 100, and (iii) 144

**☛ Related Questions:**

- The following numbers are obviously not perfect squares. Give reason. (i) 1057 (ii) 23453 (iii) 7928 (iv) 222222 (v) 64000 (vi) 89722 (vii) 222000 (viii) 505050
- The squares of which of the following would be odd numbers? (i) 431 (ii) 2826 (iii) 7779 (iv) 82004
- Observe the following pattern and find the missing digits. 112 = 121 1012 = 10201 10012 = 1002001 1000012 = 1....2....1 100000012 = ...........
- Observe the following pattern and supply the missing numbers. 112 = 121 1012 = 10201 101012 = 102030201 10101012 = ? ?2 = 10203040504030201

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