How many integers 1≤N≤1000 can be written both as the sum of 26 consecutive integers and as the sum of 13 consecutive integers? Details and assumptions The consecutive integers are allowed to be a mix of negative integers, 0 and positive integers (as long as they are consecutive).
please give
That's cheating, and if you don't know how to solve this one, wait till you see the really hard ones !
pls tell
since they are consecutive integers, the common difference in both series must be 1 d = 1 let the first term of the longer series be a let the first term of the shorter series be b sum(n) = (n/2)(2a + (n-1)d ) (26/2) (2a + 25(1) ) = (13/2)(2b + 12(1) ) 26(2a+25) = 13(2b+12) 52a + 650 = 26b + 156 52a + 494 = 26b b = (52a + 494)/26 = 2a + 19 if a=1 , b = 21 Long series: 1+2+3+...+26 = 351 short series: 21+22+..+33 = 351 if a=2 , b = 23 Long series: 2+3+..+27 = 377 short series: 23+24+...+35 = 377 ..... the last term in the sort series has to be ≤ 1000 , and clearly odd, making b = 987 and a = 484 short series: 987 + 988 + ... + 999 = 12909 long series : 484+485+...+509 = 12909 since a goes from 1 to 484 , there are 484 such series. I will leave it up to you to answer the question.
i got itss 38
Join our real-time social learning platform and learn together with your friends!