Question

Erica and Naomi are both pledging study hours as they prepare for theirAlgebra 1 EOC next week. Erica says that she is going to study fifteen minutesthe first night of this week and then double how much she studies every dayfor the next seven days. Naomi says she is going to study 3 hours the first daythis week and then is going to add on thirty minutes each day for the nextseven days.Part A: Write a recursive and explicit formula for each girl’s study pledge. Erica:Naomi:

Answer 1

we know that

Erica

The sequence in minute is

15,30,60,120,240,480,960

This is a geometric sequence

where

r=30/15=2 ----> common ratio

the recursive formula For n>1 is equal to

$\begin{gathered} a_n=a_{(n-1)}*r \\ a_n=a_{(n-1)}*2 \end{gathered}$

Find out the explicit formula

$a_n=a_1*r^{(n-1)}$

where

a1=15

r=2

$a_n=15*2^{(n-1)}\text{ ----> explicit formula}$

Naomi

we have the sequence in hours

3 3.5 4 4.5 5 5.5 6

This is an arithmetic sequence

where

d=3.5-3=0.5 ----> the common difference

the recursive formula For n> 1 is equal to

$\begin{gathered} a_n=a_{(n-1)}+d \\ a_n=a_{(n-1)}+0.5 \end{gathered}$

Find out the explicit formula

$a_n=a_1+d(n-1)$

where

a1=3

d=0.5

substitute

$\begin{gathered} a_n=3+0.5(n-1) \\ a_n=3+0.5n-0.5 \\ a_n=0.5n+2.5\text{ ----> explicit formula} \end{gathered}$