# Number Series

1. The sum of first 25 natural numbers is

(a) 325

(b) 327

(c) 320

(d) 376

**Answer: (a)**

**Explanation:**

1+2+3+…..+25

Sum of the First n Natural numbers

The symbol indicates a summation to be carried out.

= 25×13

= 325

2. Find the sum of 79 consecutive even numbers

(a) 7570

(b) 3560

(c) 6320

(d) 5520

**Answer: (c)**

**Explanation:**

2+4+6+. . . +158 (?79th even number is 79×2=158)

= 2(1+2+3+. . . +79)

= 79 × 80 = 632

3. The sum of first 25 whole numbers is

(a) 300

(b) 325

(c) 375

(d) 385

**Answer: (a)**

**Explanation:**

Whole numbers are starting from zero.

So, the sum of numbers from 0 to 24

4.

(a) 9070

(b) 7090

(c) 8060

(d) 6080

**Answer: (a)**

**Explanation:**

Sum of the squares of the First n Natural numbers,

= 9455-385

= 9070

5. The sum is equal to: [SSC Grad. 2000]

(a) 2295

(b) 2425

(c) 2495

(d) 2925

**Answer: (a)**

**Explanation:**

Sum of the Cubes of the First n Natural Numbers

=3025-100

=2925

6. Find the next nearest number in A.P: 2, 2. 5, ( ). .

(a) 3

(b) 5

(c) 4

(d) 9

**Answer: (a)**

**Explanation:**

If a constant quantity is added to or subtracted from each term of a given A.P, we get another A.P.

Example: 17, 20, 23, … is an A.P. Add 5 to each term

The general form of the A.P is a, a+d, a+2d, a+3d, . . .

Let us denote the sum to n-terms as Sn,

Then Arithmetic progression=2, 2. 5, ( )

d=2. 5-2=0. 5

- p=a, (a+d), (a+2d), …
- p=2, 2+0. 5, 2+ (2(0. 5)), … = 2, 2. 5, 3

So, next term is 3.

7. Sum of the series 5+10+15+20+ . . . is 240. Number of terms of the series is,

(a) 17

(b) 16

(c) 15

(d) 14

**Answer: (c)**

**Explanation:**

So, total number of terms is 15.

8. How many terms are in 4, 8, 16,… 2097152

(a) 20

(b) 19

(c) 18

(d) 21

**Answer: (a)**

**Explanation:**

4, 8, 12 . . . 2097152 is G. P

r=8/4=2, a=4

n-1 = 19; n=20

9. If n is odd, then sum of n odd numbers is 625 and sum of n even numbers is 600 then find number of natural numbers

(a) 44

(b) 48

(c) 49

(d) None of these

**Answer: (c)**

**Explanation:**

If n is odd then number of odd numbers

Sum of odd numbers

n =25

Sum of even number=n (n+1) = 600

n=24, 25

(n+1) is odd number

Therefore total number of odd number=odd number + even number

= 24 + 25 = 49

10. The sum of four numbers is 64. If you add 3 to the first number, 3 is subtracted from the second number, the third is multiplied by 3 and the fourth is divided by three, then all the results are equal. What is the difference between the largest and the smallest of the original numbers? [Bank 2000]

(a) 32

(b) 27

(c) 21

(d) cannot be determined

**Answer: (b)**

**Explanation:**

Let the number be a, b, c and d

Substituting these values in eq1