For the sequence 9, 6, 3, 0:
1. Find the common difference or ratio.
2. Determine the explicit formula.
3. Determine the recursive formula.
Answer (2)
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, ..
The common difference of the sequence is -3. The explicit formula is T n = 12 − 3 n , and the recursive formula is T 1 = 9 ; T n = T n − 1 − 3 for 1"> n > 1 .
;
