Question

Any help please? For extra credit

Answer 1

see explanation

Explanation:

(a)

A recursive formula allows any term in the sequence to be found by adding the common difference d to the previous term.

Here d = - 4 , then recursive formula is

`a_(n)` =
`a_(n-1)` - 4 with a₁ = 2

(b)

The explicit formula for an arithmetic sequence is

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 2 and d = - 4, thus

`a_(n)` = 2 - 4(n - 1) = 2 - 4n + 4 = 6 - 4n ← explicit formula

(c)

Using the recursive formula

a₁ = 2

a₂ = 2 - 4 = - 2

a₃ = - 2 - 4 = - 6

Using the explicit formula

a₅ = 6 - 4(5) = 6 - 20 = - 14

a₁₀ = 6 - 4(10) = 6 - 40 = - 34

a₁₀₀ = 6 - 4(100) = 6 - 400 = - 394