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User Mkln
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Explicit: t(n) = (n + 1)(n/2) ; Recursive:t(n) = t(n -1)+ n ; t(1) = 1,

This is a quadratic function because it takes two levels of differences.

1 3 6 10

2 3 4

1 1

To find an explicit formula [if you don’t already know this as the triangular numbers] is to look at a pattern of products.

1 = 2 x .5

3 = 3 x 1

6 = 4 x 1.5

10 = 5 x 2

the next number should be 6 x 2.5 = 15

The explicit formula is (n+1)(n/2) or (n^2 +n)/2 [The formula for triangular numbers]

For the recursive formula look at the 1st differences, 2,3,4,… the formula for this is n + 1. But you will be using the term before, or t(n-1) so (n + 1) for (n - 1) becomes just “n”

t(n)= t(n-1) + n

You know the 4th term to find the 5th term, take the 4th term and add 5

10 + 5 = 15
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