For the sequence 9,6,3,0 find the common difference or ratio, the explict formula, recursive formula

9, 6, 3, 0

a = Ist Term = 9.

Common difference is = T2 - T1 = 6 - 9 = - 3.

The sequence is an Arithmetic Progression AP = a + (n-1) * d

Tn = a + (n-1) * d

Tn = 9 + (n-1) * (-3). Expand and simplify.

Tn = 9 - 3n + 3.

Tn = 12 - 3n.

Hence the recursive formula is = 12 - 3n. Where n = position of term. n = 1, 2, 3, ...