Question

⭐️ Help?.............

Answer 1

Option C. is the correct option.

Explanation:

The given sequence is 14.5, 11, 7.5, 4, 0.5.......

we have to find the explicit formula of the given sequence.

First we will find whether the sequence is arithmetic of geometric.

For Arithmetic sequence

Common difference D1 = 11 - 14.5 = -3.5

D2 = 7.5 - 11 = -3.5

D3 = 4 - 7.5 = -3.5

Here D1 = D2 = D3 = (-3.5)

Therefore the sequence is an arithmetic sequence.

As we know explicit formula of an arithmetic sequence is defined as

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

Here n = number of term

a = first term

d = common difference

By putting values of a and d in the explicit formula

`a_(n)= 14.5+(n-1)(-3.5)`

`a_(n)=14.5-(n-1)(3.5)=14.5-3.5n+3.5=18-3.5n`

Option C.
`a_(n)=18-3.5n` will be the explicit formula.

Answer 2

The correct answer is C.

This is because you need a first term that equals 14.5, for when n = 1.

So, you can determine this by using n=1 in each equation until you find one that works. When you stick 1 in for n in answer C, it looks like this:
18 - 3.5n
18 - 3.5(1)
18 - 3.5
14.5 ---> This is the answer that we are looking for.

This will not work for any of the other options.