Find the fifth term of the sequence a sub1 = 12, a sub n+1 = a sub n / n+1?
a)1/10
b)1/30
c)12/5
d)1/2
12,6,2,1/2, 1/2 divided by 5
To find the fifth term of the sequence, we need to apply the given recursive formula: a sub n+1 = a sub n / (n+1).
Starting with the first term, a sub 1 = 12, we apply the formula to find the second term:
a sub 2 = a sub 1 / (2+1) = 12 / 3 = 4
Next, we use the formula again to find the third term:
a sub 3 = a sub 2 / (3+1) = 4 / 4 = 1
Continuing, we find the fourth term:
a sub 4 = a sub 3 / (4+1) = 1 / 5 = 1/5 = 0.2
Finally, to find the fifth term, we apply the formula once more:
a sub 5 = a sub 4 / (5+1) = 1/5 / 6 = 1/5 * 1/6 = 1/30
Therefore, the fifth term of the sequence is 1/30.
The correct answer is b) 1/30.