Question

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

Answer 1

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, ..