SOLUTION: find the missing number 1,2,6,22,86 --,---,----,? and which rule is used ?

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: find the missing number 1,2,6,22,86 --,---,----,? and which rule is used ?      Log On


   

Question 333969: find the missing number
1,2,6,22,86 --,---,----,?
and which rule is used ?
Answer by jrfrunner(365) About Me  (Show Source):
You can put this solution on YOUR website!
in this series, a%5Bi%5D=a%5Bi-1%5D++%2B4%5E%28i-2%29 where a%5B0%5D=3%2F4 and i>0
---
for i=1, a%5B1%5D=a%5B0%5D%2B4%5E-1=%283%2F4%29%2B%281%2F4%29=1
for i=2, a%5B2%5D=a%5B1%5D%2B4%5E0=1%2B1=2
for i=3, a%5B3%5D=a%5B2%5D%2B4%5E1=2%2B4=6
for i=4, a%5B4%5D=a%5B3%5D%2B4%5E2=6%2B16=22
for i=5, a%5B5%5D=a%5B4%5D%2B4%5E3=22%2B64=86
----
for i=6, a%5B6%5D=a%5B5%5D%2B4%5E4=86%2B256=342
for i=7, a%5B7%5D=a%5B6%5D%2B4%5E5=342%2B1024=1366
for i=8, a%5B8%5D=a%5B7%5D%2B4%5E6=1366%2B4096=5462