The sum of the odd numbers in an even-ending sequence is 2/5 of the total sum. The sum of an arithmetic sequence is
Sn = n(a1 + an)/2
Sn = n(a1 + an)/5
Sn = 400(1+400)/5
Sn = 32080
* * * * *
Very convincing but totally incorrect!
Simply try it out for the first 2 consecutive odd numbers:
1 + 3 = 4
1 + 2 + 3 = 6 but 4 is not 2/5 of 6!
The correct answer:
The nth odd number is 2n - 1
The sum of the 1st and 400th odd numbers is 2*1-1 + 2*400-1 = 2*401 - 2 = 2*400 = 800
The sum of the 2nd and 399th odd numbers is 2*2-1 + 2*399-1 = 2*401 - 2 = 2*400 = 800
there are 200 such pair so the grand total is 800*200 = 160,000
Chat with our AI personalities
The answer is 20*20 = 400
The sum of the first 30 consecutive odd numbers is 900.
The sum of the first 900 consecutive odd numbers is 810,000.
The sum of the first 350 consecutive odd numbers is 122,500.
The sum of the first 30 consecutive odd numbers is 900.