Sum of First n Natural Numbers MCQ Quiz - Objective Question with Answer for Sum of First n Natural Numbers - Download Free PDF

Concept:

If a1, a2, a3,...are in GP with common ratio r, 

If a be the first term, r be the common ratio of a GP then,

Calculation:

Calculation:

Let required sum is S.

⇒ S =

⇒ S =

⇒ S = 

⇒ S = 

Threfore, a = 1/2 and r = 1/2

We know that the sum of the n^th term of GP (r

⇒ S = 

⇒ S =           (∵ 1/aⁿ = a^-n)

⇒ S = n - 1 + 2-n

∴ S = n + 2-n -1

Concept:

1. The nth term of the A.P. is given by:

an = a + (n – 1) d

2. The sum of n terms of an AP with first term a and common difference d is given by: 

      ----(1)

Or

Where,

an = nth term and l = Last term

Calculation:

Given: 

d = 3/2

n = 25

a = 3

From equation (1);

Concept: 

Sum of consecutive numbers from 1 to n: .

Calculation:

The sum of the first 24 terms of the given series can be written as:

.

Concept use:

The Sum of First n odd Numbers is n².

Explanation:

The sum of the first 20 consecutive positive odd numbers is 20² (by the Formula of sum of First n odd Numbers)

Now, Divide by 20².

∴ 20²/20² = 1

Hence, The Correct Answer is option 1.

Given:

Σn = 36

Formula used:

Σn = n(n + 1) / 2

Where,

Σn = sum of the first n natural numbers

Calculation:

Σn = 36

We need to find n such that

n(n + 1) / 2 = 36

⇒ n(n + 1) = 72

⇒ n² + n - 72 = 0

⇒ (n - 8) (n + 9) = 0

Taking the positive value, n - 8 = 0 

So, n = 8

Concept: 

Sum of consecutive numbers from 1 to n: .

Calculation:

The sum of the first 20 terms of the given series can be written as:

.

Concept: 

Sum of consecutive numbers from 1 to n: .

Calculation:

The sum of the first 18 terms of the given series can be written as:

3 + 6 + 9 + 12 + 15, ....... 

⇒ 3(1 + 2 + 3 + 4 + 5 + ....)

⇒  

Concept: 

Sum of consecutive numbers from 1 to n: .

Calculation:

The sum of the first 24 terms of the given series can be written as:

.

The correct answer is 

Concept: 

Sum of consecutive numbers from 1 to n: .

Calculation:

The sum of the first 24 terms of the given series can be written as:

.

Concept: 

Sum of consecutive numbers from 1 to n: .

Calculation:

The sum of the first 12 terms of the given series can be written as:

.

Concept:

1. The nth term of the A.P. is given by:

an = a + (n – 1) d

2. The sum of n terms of an AP with first term a and common difference d is given by: 

      ----(1)

Or

Where,

an = nth term and l = Last term

Calculation:

Given: 

d = 3/2

n = 25

a = 3

From equation (1);

Formula Used: 

Sum of square of n numbers = 

Sum of n terms = 

Calculation:      

a₁ = 1

a₂ = 1 + 8 = 9

a₃ = 9 + 8 + 7 = 24

a₄ = 24 + 8 + 7 + 7 =  46

So, then K^th term will be:

⇒ a_k = 1 + 8(k - 1) + 7

⇒ a_k = 7k²/2 - 5k/2

Sum of first n term:

The correct option is 4 i.e.    

Formula used:

sum of first n natural numbers = n(n +1)/2

a^m × aⁿ = a^{m + n}

Calculation:

Sum of natural numbers upto 10 = 10(10 + 1)/2 = 55

Then, according to the question:

5 × 52 × 53....(10 terms) = 5⁵⁵

∴ 5 × 52 × 53....(10 terms) = 5⁵⁵

Given:

Σn = 36

Formula used:

Σn = n(n + 1) / 2

Where,

Σn = sum of the first n natural numbers

Calculation:

Σn = 36

We need to find n such that

n(n + 1) / 2 = 36

⇒ n(n + 1) = 72

⇒ n² + n - 72 = 0

⇒ (n - 8) (n + 9) = 0

Taking the positive value, n - 8 = 0 

So, n = 8

Concept: 

Sum of consecutive numbers from 1 to n: .

Calculation:

The sum of the first 12 terms of the given series can be written as:

.