Answer:
You will receive 262,144 pennies after completing the 9th job.
Step-by-step explanation:
Given:
Payment for 1st job = 4 pennies
The payment is quadrupled after this for each job completed.
Payment after 2 jobs = 16 pennies
Payments after 3 jobs = 64 pennies
To find the number of pennies you will receive after the 9th job.
Solution:
Let [tex]a_1[/tex] represent the payment after 1st job.
[tex]a_1=4[/tex]
[tex]a_2=16[/tex]
[tex]a_3=64[/tex]
The sequence is in geometric sequence with common ratio = 4
The n[tex]th[/tex] term of a geometric sequence is given as:
[tex]T_n=a_1r^{(n-1)}[/tex]
For the sequence:
[tex]a_1=4[/tex]
[tex]n=9[/tex]
[tex]r=4[/tex]
For the sequence we need the payment after 9th job. So, we are finding [tex]T_9[/tex].
[tex]T_9=4(4)^{(9-1)}[/tex]
[tex]T_9=4(4)^{8}[/tex]
[tex]T_9=4(65536)[/tex]
[tex]T_9=262144[/tex]
Thus, you will receive 262,144 pennies after completing the 9th job.
Answer:
add four and nine in the first to boxes and in the second column put 262144
Step-by-step explanation:
Basically if you do 2 grooming jobs its four to the 2nd power. 3 grooming jobs would be 4 to the third power. 4 would be 4 to the fourth power and so on. If she does 9 grooming jobs it would be 4 to the 9th power. 4 to the 9th power would look like 4x4x4x4x4x4x4x4x4 which would equal 262,144.
