Problem 1 :
Find the sum of
1 + 3 + 5 + ........ to 40 terms
Problem 2 :
Find the value of
1 + 3 + 5 + ........ + 55
Problem 3 :
Find the value of
21 + 23 + 25 + ........ + 99
Problem 4 :
Find the sum of
2 + 6 + 10 + ........ to 50 terms
Problem 5 :
Find the sum of
2 + 6 + 10 + ........ + 246
Problem 6 :
If 1 + 3 + 5 + ........ + k = 1444, then find k.
Problem 7 :
If 1 + 3 + 5 + ........ to k terms = 676, then find k.
Problem 8 :
Find the average of first 25 odd natural numbers.
1. Answer :
Using 1 + 3 + 5 + ........ to n terms = n2,
1 + 2 + 3 + ........ + 40 terms = 402
= 1600
2. Answer :
Using 1 + 3 + 5 + ........ + l = [(l + 1)/2]2,
1 + 2 + 3 + ........ + 55 = [(55 + 1)/2]2
= [56/2]2
= 282
= 784
3. Answer :
21 + 23 + 25 + ........ + 99 :
= (1 + 2 + 3 + ........ + 99) - (1 + 2 + 3 + ........ + 19)
Using 1 + 3 + 5 + ........ + l = [(l + 1)/2]2,
= [(99 + 1)/2]2 - [(19 + 1)/2]2
= [100/2]2 - [20/2]2
= 502 - 102
= 2500 - 100
= 2400
4. Answer :
2 + 6 + 10 + ........ to 50 terms :
= 2(1 + 3 + 5 + ........ to 50 terms)
Using 1 + 3 + 5 + ........ to n terms = n2,
= 2(502)
= 2(2500)
= 5000
5. Answer :
2 + 6 + 10 + ........ + 246 :
= 2(1 + 3 + 5 + ........ + 123)
Using 1 + 3 + 5 + ........ + l = [(l + 1)/2]2,
= [(123 + 1)/2]2
= [124/2]2
= 622
= 3844
6. Answer :
1 + 3 + 5 + ........ + k = 1444
Using 1 + 3 + 5 + ........ + l = [(l + 1)/2]2,
[(k + 1)/2]2 = 1444
[(k + 1)/2]2 = 382
(k + 1)/2 = 38
Multiply each side by 2.
k + 1 = 76
Subtract 1 from each side.
k = 75
7. Answer :
1 + 3 + 5 + ........ to k terms = 676
Using 1 + 3 + 5 + ........ to n terms = n2,
k2 = 676
k2 = 262
k = 26
8. Answer :
Using 1 + 3 + 5 + ........ to n terms = n2, to find the sum of first 25 odd natural numbers.
1 + 2 + 3 + ........ to 25 terms = 252
= 625
Average of first 25 odd natural numbers :
= (Sum of first 25 odd natural numbers)/25
= 625/25
= 25
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