5) Fill in the gaps in this sequence: -8, -19.-30,_ , _ .
a. What type of sequence is this, Geometric or Arithmetic? Explain.
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b. Write an explicit formula for this sequence.
c. Write a recursive formula for this sequence.
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d. Find the 30th term.

The missing two terms are -41 and -52

a. The sequence is arithmetic

b. The explicit formula for the sequence is

c. The recursive formula for this sequence is = -8; = + -11

d. The 30th term is -327

Step-by-step explanation:

The terms of the sequence are -8 , -19 , -30

∵ -19 - (-8) = -19 + 8 = -11

∵ -30 - (-19) = -30 + 19 = -11

- That means there is a constant difference between each two

    consecutive terms

∴ -30 + -11 = -41

∴ -41 + -11 = -52

∴ The missing two terms are -41 and -52

a.

∵ There is a constant difference between each two

   consecutive terms

∴ The sequence is arithmetic

b.

The explicit formula of the nth term of an arithmetic sequence is , where a is the first term and d is the constant difference between each two consecutive term

∵ The first term is -8

∴ a = -8

∵ The constant difference is -11

∴ d = -11

- Substitute them in the formula above

∴

- Simplify it by multiplying (n - 1) times -11

∴

∴

∴ The explicit formula for the sequence is

c.

The recursive formula of the arithmetic sequence is:

= first term; = + d, where d is the common difference between each two consecutive terms

∵ The first term is -8

∴

∵ The constant difference is -11

∴ d = -11

∴ = -8; = + -11

∴ The recursive formula for this sequence is = -8; = + -11

d.

∵ The term is 30th

∴ n = 30

- Substitute it in the explicit formula of the sequence

∴

∴

∴  

∴ The 30th term is -327

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step-by-step explanation: