We can categories number

**Natural Numbers (Positive Integers)** **:- **All numbers from 1 to infinity which are used for counting are called natural numbers. It is denoted by N.

Ex - 1, 2, 3, 4. . . . . ∞

**Whole Numbers :-** When 0 is included in natural numbers it s called whole numbers.

Ex - 0, 1, 2, 3 . . . .∞

**Negative Integers :- **Negative integers include all negative number from -∞ to -1.

Ex - -∞ . . . . -4, -3, -2, -1

**Integers :- **Group of natural number, zero and negative number is integer.

Ex - -∞ . . . . -4, -3, -2, -1, 0, 1, 2, 3 . . . .∞

**Even Numbers :- **Numbers which are divided by 2 is known as even numbers.

Ex - 2, 4, 6, 8. . . . , 1, 2, 3 . . . .∞

**Odd Numbers :-** Numbers which are not divided by 2 are called odd numbers.

Ex - 1, 3, 5,7 . . . . ∞

**Composite Numbers :- **Numbers which are divided by other than 1 and self are composite number.

Ex - 4, 6, 9, 10

**Prime Numbers :-** Number which are not divided by other than 1 and itself are prime number.

Ex - 2 , 3, 5

**Co-prime Numbers :-** A pair in which both numbers are prime is called co-prime.

Ex - (3, 5), (7, 11)

**Rational Numbers :- **Numbers in form of p/q and q ≠ 0 are rational number.

Ex - 7, 11, 3/4, 7/11

**Irrational Numbers :-** Numbers which can not be write in form of p/q are irrational number.

Ex - √2, √3, π

**Real Numbers :- **Numbers which contains both rational and irrational numbers are real number.

Ex - 7, 11, 3/4, 7/11,√2, √3, π

**Consecutive Numbers :- **Numbers that follow continuously from smallest to largest** **are consecutive numbers and difference between each number will be 1.

if one integer is X then other consecutive will be X+1, X+2 and so on.

**Consecutive Even Numbers :- **Even numbers that follow other continuously are consecutive even number and difference between two consecutive number always be 2. If one even number is X then others are X+2, X+4, and so on.

**Consecutive Odd Numbers :-** odd numbers that follow other continuously are consecutive odd number and difference between two consecutive number always be 2. If one odd number is X then others are X+2, X+4, and so on.

### Finding Sum of consecutive Numbers

if there are n consecutive number from 1

1+2+3+4+5 . . . . .n

sum = n(n+1)/2

watch video for detailed explanation

**Some questions for practice**

**Q 1. **Find sum of 1 + 2 + 3 + 4 + 5 . . . . . . . . . . . . + 100.

**a. **2500 **b. **5050 **c. **10100 **d. **4500

**Q 2. **Sum of 2 + 4 + 6 + 8 . . . . . . . . . . . + 80.

**a. **5050 **b. **1600 **c. **3280 **d. **1640

**Q 3. ** Sum of first 10 multiple of 3.

**a. **165 **b. **44 **c. **55 **d. **330

**Q 4. **Sum of 101 + 102 + 103 + 104 . . . . . . . . .+ 200.

**a. **1500 **b. **15025 **c. **15050 **d. **25000

**Q 5. **if** **sum of 1 + 2 + 3 . . . . . . + 10 = 55 then sum of 5 + 10 + 15 + 20 . . . . . . + 50 is -

**a. **250 **b. **655 **c. **275 **d. **300

**Q 6. ** 1 + 2 + 3 + 4 . . . . . . + 23 + 24 + 25 + 24 +23 . . . . . 2 + 1 is equal to -

**a. **1500 **b. **625 **c. **350 **d. **600

**Q 7. **Sum of 1 + 2 + 3 + 4 . . . . . . . + 200 is -

**a. **20200 **b. **10100 **c. **5050 **d. **20100

**Q 8. **Sum of all positive multiple of 7 less than 50 is

**a. **196 **b. **700 **c. **392 **d. **146

**Q 9. **Sum of how many terms in series 1 + 2 + 3 + 4 . . . is 1275

**a. **25 **b. **100 **c. **51 **d. **50

**Q 10.** Sum of how many terms in series 1 + 2 + 3 + 4 . . . is 5050

**a. **50 **b. **51 **c. **100 **d. **101

**Answer Key**

**Q 1. **b **Q 2. **d **Q 3.** a **Q 4. **c** ** **Q 5.** c

**Q 6. **b **Q 7. **d **Q 8.** a **Q 9. **d** ** **Q 10.** c