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
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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
20
3, -6, 12, 4, 20, ?
25 is the next number that appears in that sequence.
20
10 The sequence is given by xn = 60/n
56
10. (Don't ask why.)
16
22
92 - 18 = 72 72 - 16 = 56 56 - 14 = 42 42 - 12 = 30 30 - 10 = 20 20 is the next number in the sequence.
13 20 12
next in the sequence: 10,20,30,20