0
Want this question answered?
Be notified when an answer is posted
Add your answer:
Earn +20 pts
What is the 34th number in this sequence 2 6 12 20?
The 34th number is 1190. First number is 2 = 2n where n = 1 Second number is 4 + 2 = 2n + 2(n-1) where n = 2 Third number is 6 + 4 + 2 = 2n + 2(n-1) + 2(n -2) where n = 3 Fourth number is 8 + 6 + 4 + 2 = 2n + 2(n-1) + 2(n-2) + 2(n-3) where n = 4 . . . In general the nth number is 2n + 2(n-1) + 2(n-2) + 2(n-3) + ..... + 2(n-n+1) and In general the nth number is 2n + 2(n-1) + 2(n-2) + 2(n-3) + ..... + 2(1) Take 2 as a common factor and we get nth number = 2(n + n -1 + n -2 + n -3 + ..... + 1) which is = 2(1 + 2 + 3 + ..... + n-3 + n-2 + n-1 + n) = 2(sum of n numbers starting with 1) But sum of n numbers starting with 1 is (n)(n+1)/2 Hence nth number in general is (2)(n)(n+1)/2 = n(n+1) Hence 34th number would be 34(34+1) = 34x35 = 1190
