Question

Your friend owes you some money. He tells you that he'll pay you a penny today and triple the amount each day. If he follows his plan, how much will he pay you on day 12?

Answer 1

`3^(11)`

Explanation:

Given you will receive a penny today and the amount is tripled each day

so if we write down each day payment we get a geometric progression.

Day 1=1

Day 2=3

Day 3=9

..

the series is 1,3,9,...

it is a geometric progression with a=1 r=3

we know that the general form of nth term in a GP is t(n)=a
`r^(n-1)`

t(n)=1*
`3^(n-1)`

now we need to find the amount on 12th day by substituting n=12

we get

t(12)=
`3^(11)`

He will pay
`3^(11)` on the 12th day .