Question

The following recursive formula represents the value of the jackpot in a game show after each round, in hundreds of dollars. an={1,ifn=1an−1+5,ifn>1 Write the explicit formula for the prize value and use it to calculate the value of the prize in round 8. an =  +  (n – 1) Value of jackpot in round 8: $ 

Answer 1

Problem

The following recursive formula represents the value of the jackpot in a game show after each round, in hundreds of dollars. an={1,ifn=1an−1+5,ifn>1 Write the explicit formula for the prize value and use it to calculate the value of the prize in round 8. an = + (n – 1) Value of jackpot in round 8: $ ​

Solution

For this case we have the following recursive formula:

an = 1 if n=1

an = an-1 +5 for n>1

And of we replace n =8 we got:

a8 = a7 + 5

We also know that:

a2 = 1 +5=6

a3= 6+5= 11

a4= 11+5= 16

a5= 16+5= 21

a6= 21+5= 26

a7= 26+5= 31

Then the final answer would be:

a8 = 31+ 6= 37