Question

Please help me right away with both problems.

Answer 1

Problem 3.

Use the positive integers for n in increasing order starting with 1. First use n = 1, then n = 2, then n = 3, etc. Replace n with an integer, and solve for an.

`a_n = 3n + 2`

`a_1 = 3(1) + 2 = 3 + 2 = 5`

`a_2 = 3(2) + 2 = 6 + 2 = 8`

`a_1 = 3(3) + 2 = 9 + 2 = 11`

`a_4 = 3(4) + 2 = 12 + 2 = 14`

Answer: 5, 8, 11, 14

Problem 4.

The first number in the sequence is 23. Each term is then 6 less than the previous term.

`t_1 = 23`

`t_2 = 23 - 6 * 1`

`t_3 = 23 - 6 * 2`

Start with 29 - 6, then 29 - 12, 29 - 18.

`t_1 = 29 - 6 = 29 - 6 * 1`

`t_2 = 29 - 12 = 29 - 6 * 2`

`t_3 = 29 - 18 = 29 - 6 * 3`

`t_n = 29 - 6n`

Answer:
`t_n = 29 - 6n`

Answer 2

3) aₓ = 3x + 2

Plug in numbers for x (for example, 1,2,3,4).

a₁ = 3(1) + 2; a₁ = 3 + 2; a₁ = 5

a₂ = 3(2) + 2; a₂ = 6 + 2; a₂ = 8

a₃ = 3(3) + 2; a₃ = 9 + 2; a₃ = 11

a₄ = 3(4) + 2; a₄ = 12 + 2; a₄ = 14

5, 8, 11, 14, or (C) is your answer

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4) 23, 17, 11, 5

Plug in the following numbers to the equations until they match.

C) tₐ = 29 - 6n

when n = 1:

tₐ = 29 - 6(1) ; tₐ = 29 - 6 ; tₐ = 23

tₐ = 29 - 6(2) ; tₐ = 29 - 12 ; tₐ = 17

etc.

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hope this helps