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2 short questions 100 point pls help

2 Short Questions 100 Point Pls Help class=

Sagot :

So

Common difference

  • t_3-t_2
  • 6.8-5
  • 1.8

#4

The formula is

  • a_n=10n-14

Put n=8

  • a_8=10(8)-14=80-14=66
Semsee45idn

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:

  • a = 138

b) The common difference is the amount she deposits each week:

  • d = 55

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]

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