Question

Find the first five term of the sequence where s_(1)=9 and s_(n)=(3)/(5)s_(n-1),n>=2 Classify the sequence as arithmatic, geometric, fibonacci or none Be sure to type 5 terms with commas then classify it.

Answer 1

The first five terms of the sequence are 9, 27/5, 81/25, 243/125, 729/625. The sequence is geometric because each term is obtained by multiplying the previous term by a common ratio (3/5 in this case).

Step-by-step explanation:

The sequence is defined by the formula sn = (3/5)sn-1, where s1 = 9 and n >= 2. To find the first five terms of the sequence, we can use the formula recursively.

1. s1 = 9
2. s2 = (3/5)s1 = (3/5)(9) = 27/5
3. s3 = (3/5)s2 = (3/5)(27/5) = 81/25
4. s4 = (3/5)s3 = (3/5)(81/25) = 243/125
5. s5 = (3/5)s4 = (3/5)(243/125) = 729/625

The first five terms of the sequence are 9, 27/5, 81/25, 243/125, 729/625.

The sequence is geometric because each term is obtained by multiplying the previous term by a common ratio (3/5 in this case).