Respuesta :
The asnwer to the following set of questions are as follows:
1. The 8th term of the sequence would be 1.
2. A. an=15.5−2.5n
3. The coin collector will have 1350 coins after 34 months
4. The recursive rule for an=3n+5 would be a1=8;an=an−1+3
I hope my answer has come to your help. God bless and have a nice day ahead!
1. The 8th term of the sequence would be 1.
2. A. an=15.5−2.5n
3. The coin collector will have 1350 coins after 34 months
4. The recursive rule for an=3n+5 would be a1=8;an=an−1+3
I hope my answer has come to your help. God bless and have a nice day ahead!
Answer:
Step-by-step explanation:
(1) Using the rule [tex]a_n=25-3n[/tex]
put n=8 in the above formula we get
[tex]a_8=25-3(8)=1[/tex]
Hence, [tex]a_8=1[/tex]
(2) The given sequence has common difference -2.5
common difference that is [tex]d=a_2-a_1[/tex]
We will use the formula of AP which is
[tex]a_n=a+(n-1)d[/tex]
Here, a= 13, d=-2.5 and n=n on substituting the values in the formula we get
[tex]a_n=13+(n-1)(-2.5)[/tex]
[tex]a_n=15.5-2.5n[/tex]
Hence, Option A
(3)From the given information we can conclude
[tex]a=1044,d=9,n=34[/tex]
We have to find [tex]a_n[/tex]
On substituting the values we get
[tex]a_n=1044+(34-1)(9)[/tex]
[tex]a_n=1044+297[/tex]
[tex]a_n=1341[/tex] coins the coin collector will have.
(4) Recursive rule for [tex]a_n=3n+5[/tex] will be
Put n=1 in the given formula we get
[tex]a_1=3(1)+5=8[/tex]
When n=2 we get
[tex]a_2=3(2)+5=11[/tex]
When n=3 we get
[tex]a_3=3(3)+5=14[/tex]
Hence, option A that is [tex]a_1=8;a_n=a_{n-1}+3[/tex]
