Question

The Gaineys and the Arnolds are saving money for a trip to Utah to go snowboarding. The Arnolds are going to save a nickel on the first day of the month and then double the amount each day for a month. The Gaineys are going to start their savings by saving
$10
on the first day and then
$10
each day of the month.

Part A: Write a recursive and explicit formula for each option.

Answer 1

Write a recursive and explicit formula for each option.

• The Arnolds

Save a nickel on the first day of the month and then double the amount each day for a month

=> a1 =0.05

=> a2 = a1* 2 = 0.05*2

=> a3 = a2*2 = a1* 2*2

..............................................

=>recursive an = $a_{n-1} *2$

=> explicit an = 0.05*$2^{n-1}$

• The Gaineys

Start their savings by saving  $10  on the first day and then  $10  each day of the month

=> a1 = 10

=> a2 = a1 + 10 = 20

=> a3 = a2 +10 = 20 +10 =30

........................................................

=> recursive an = $a_{n-1} +10$

=> explicit an = 10 + 10( n-1)

Hope it will find you well.