Sum of First n Natural Numbers Worksheet

Problem 1 :

Find the value of

1 + 2 + 3 + ........ + 50

Problem 2 :

Find the value of

16 + 17 + 18 + ........ + 75

Problem 3 :

Find the sum of 

1 + 2 + 3 + ........ to 40 terms

Problem 4 :

Find the sum of

2 + 4 + 6 + ........ to 50 terms

Problem 5 :

Find the value of

2 + 4 + 6 + ........ + 256

Problem 6 :

If 1 + 2 + 3 + ........ + n = 666, then find n. 

Problem 7 :

Find the average of first 25 natural numbers. 

Problem 8 :

Find the average of first 30 natural numbers which are the multiples of 5. 

Answers

1. Answer :

Using 1 + 2 + 3 + ........ + n = n(n + 1)/2, 

1 + 2 + 3 + ........ + 50 = 50(50 + 1)/2

= 50(51)/2

= 25(51)

= 1275

2. Answer :

16 + 17 + 18 + ........ + 75 : 

= (1 + 2 + 3 + ........ + 75) - (1 + 2 + 3 + ........ + 15)

Using 1 + 2 + 3 + ........ + n = n(n + 1)/2, 

= 75(75 + 1)/2 - 15(15 + 1)/2

= 75(76)/2 - 15(16)/2

= 75(38) - 15(8)

= 2850 - 120

= 2730

3. Answer :

Because the given series is a sum of first 40 natural numbers, the last term in the series is also 40. 

1 + 2 + 3 + ........ to 40 terms = 1 + 2 + 3 + ........ to 40

Using 1 + 2 + 3 + ........ + n = n(n + 1)/2, 

= 40(40 + 1)/2

= 40(41)/2

= 20(41)

= 820

4. Answer :

2 + 4 + 6 + ........ to 50 terms : 

= 2(1 + 2 + 3 + ........ to 50 terms)

= 2(1 + 2 + 3 + ........ + 50)

Using 1 + 2 + 3 + ........ + n = n(n + 1)/2, 

= 2[50(50 + 1)/2]

= 2[50(51)/2]

= 2[25(51)]

= 2550

5. Answer :

2 + 4 + 6 + ........ + 256 : 

= 2(1 + 2 + 3 + ........ + 128)

Using 1 + 2 + 3 + ........ + n = n(n + 1)/2, 

= 2[128(128 + 1)/2]

= 2[128(129)/2]

= 2[64(129)]

= 8256

6. Answer :

1 + 2 + 3 + ........ + n = 666

Using 1 + 2 + 3 + ........ + n = n(n + 1)/2, 

n(n + 1)/2 = 666

Multiply each side by 2.

n(n + 1) = 1332

n² + n = 1332

Subtract 1332 from each side. 

n² + n - 1332 = 0

Factor and solve. 

n² + 37n - 36n - 1332 = 0

n(n + 37) - 36(n + 37) = 0

(n + 37)(n - 36) = 0

But n ≠ -37, because n is a natural number. 

Hence n = 36.

7. Answer :

Use 1 + 2 + 3 + ........ + n = n(n + 1)/2, to find the sum of first 25 natural numbers. 

1 + 2 + 3 + ........ + 25 = 25(25 + 1)/2

= 20(26)/2

= 20(13)

= 260

Average of first 25 natural numbers : 

= (Sum of first 25 natural numbers)/20

= 260/20

= 13

8. Answer :

The first natural number which is a multiple of 5 is 5.

The next numbers which are the multiples of 5 are

10, 15, 20, ........

Write the first 30 natural numbers which are the multiples of 5.

5, 10, 15, ........ to 30 terms

Find the sum of all the above numbers. 

= 5 + 10 + 15 +......... to 30 terms

= 5(1 + 2 + 3 +......... to 30 terms)

= 5(1 + 2 + 3 +......... + 30)

Using 1 + 2 + 3 + ........ + n = n(n + 1)/2, 

= 5[30(30 + 1)/2]

= 5[15(31)]

= 5[465]

= 2325

Average :

= (Sum of all 30 numbers)/30 

= 2325/30

= 77.5 

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