what is the rule and sequence of 4 14 29 49
Answers
Answered by
0
Sequence: 4, 14, 29, 49, ….
Differences: 10, 15, 20 (multiples of 5 could be 5n)
Rewrite sequence : (-1 + 5), (-1 +5 + 10), (-1 + 5 + 10 + 15)
So nth term = -1 + sigma(5n) = -1 + 5 x sigma(n)
Where Sigma(n) = sum of 1 + 2 + 3 + 4 + ………. + n
Can easily be shown that sigma(n) = n(n+1)/2
=> a(n) = -1 + 5n(n+1)/2
Differences: 10, 15, 20 (multiples of 5 could be 5n)
Rewrite sequence : (-1 + 5), (-1 +5 + 10), (-1 + 5 + 10 + 15)
So nth term = -1 + sigma(5n) = -1 + 5 x sigma(n)
Where Sigma(n) = sum of 1 + 2 + 3 + 4 + ………. + n
Can easily be shown that sigma(n) = n(n+1)/2
=> a(n) = -1 + 5n(n+1)/2
Similar questions