Question

2 short questions 100 point pls help

Answer 1

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

Answer 2

3) d = 1.8

4) a₈ = 66

5) a) 138

b) 55

c)
`a_n=55n+83`

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:
`a_n=10n-14`

To find the 8th term, substitute n = 8 into the equation:

`\implies a_8=10(8)-14`

`\implies a_8=80-14`

`\implies a_8=66`

Question 5

General form of an arithmetic sequence:

`a_n=a+(n-1)d`

where:

• 
  `a_n` 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:

`\implies a_n=138+(n-1)55`

`\implies a_n=138+55n-55`

`\implies a_n=55n+83`