Answer:
3) d = 1.8
4) a₈ = 66
5) a) 138
b) 55
c) [tex]a_n=55n+83[/tex]
Step-by-step explanation:
Question 3
The common difference of an arithmetic sequence is the difference between consecutive terms.
Therefore, to find the common difference, subtract one term from the next:
⇒ d = 5 - 3.2
⇒ d = 1.8
Question 4
Given arithmetic sequence: [tex]a_n=10n-14[/tex]
To find the 8th term, substitute n = 8 into the equation:
[tex]\implies a_8=10(8)-14[/tex]
[tex]\implies a_8=80-14[/tex]
[tex]\implies a_8=66[/tex]
Question 5
General form of an arithmetic sequence:
[tex]a_n=a+(n-1)d[/tex]
where:
- [tex]a_n[/tex] is the nth term
- a is the first term
- d is the common difference between terms
a) The first term is the initial amount Mrs Speas has in her bank account:
b) The common difference is the amount she deposits each week:
c) The iterative rule for the amount of money she has after n weeks is:
[tex]\implies a_n=138+(n-1)55[/tex]
[tex]\implies a_n=138+55n-55[/tex]
[tex]\implies a_n=55n+83[/tex]
