Expert: Josh - 3/28/2005

Question
Please help with the next probable number for each group.

0,5,5,10,15

4,7,12,20,32,49

7,2,-1, -2, -1

1/9, 1/3, 1

1, -1/3, 1/9

x, x², x³  

Thank you!

Answer
Hi Betsy,

(i)It looks like you have made a typo in "0,5,5,10,15"
I think this is an arithmetic sequence. Each term is the previous one plus five.
If we write a[0]=0,a[1]=5,a[2]=10,a[3]=15,a[4]=20.
In general, a[n]=a[n-1]+d, where a[0]=0,d=5.

(ii) quite a difficult one
4,7,12,20,32,...
first term, t[0]=4
subsequent terms, t[n]=2*t[n-1]-(2^(n-1))
try this out...
when n=1, t[1]=2*t[0]-2^0 = 2*4-1 = 7
when n=2, t[2]=2*t[1]-2^1 = 2*7-2 = 12
when n=3, t[3]=2*t[2]-2^2 = 2*12-4 = 20
when n=4, t[4]=2*t[3]-2^3 = 2*20-8 = 32
when n=5, t[5]=2*t[4]-2^4 = 2*32-16 = 48
when n=6, t[6]=2*t[5]-2^5 = 2*48-32 = 64

(iv) 1/9, 1/3, 1
Geometric series, next one is obtained by multiplying the previous term by 3.

(v) Geometric series, next one is obtained by multiplying the previous term by -1/3.

(vi) x^4