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.
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
n + 37 = 0
n = -37
n - 36 = 0
n = 36
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
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
©All rights reserved. onlinemath4all.com
May 04, 24 12:15 AM
May 03, 24 08:50 PM
May 02, 24 11:43 PM