Question

If the pattern below follows the rule "starting with one, every consecutive line has a number that is one more than twice the previous line", how many marbles must be in sixth line?

Answer 1

Answer:

$x_{6}=63$

Step-by-step explanation:

we have that

$x_{1}=1\\x_{2}=1+2x_{1}=1+2*1=1+2=3\\x_{3}=1+2x_{2}=1+2*3=1+6=7\\x_{4}=1+2x_{3}=1+2*7=1+14=15\\x_{5}=1+2x_{4}=1+2*15=1+30=31\\x_{6}=1+2x_{5}=1+2*31=1+62=63$