Question

Help me please !!!

Which explicit formula describes the arithmetic
sequence {19, 14, 9, 4, ...}

Answer 1

`a_n=19+(n-1)(-5)`

Explanation:

The explicit formula for an arithmetic sequence is
`a_n=a_1+(n-1)d` where
`a_n` is the
`n`th term and
`d` is the common difference.

In this problem, we can see that the first term of the sequence is
`a_1=19` and the common difference is
`d=-5` since 5 is being subtracted each consecutive term.

Therefore, the explicit formula that describes the given arithmetic sequence is
`a_n=19+(n-1)(-5)`

Answer 2

option 2

Explanation:

Let { a1, a2, a3, a4, ... } be the sequence.

now the 1st term (a1) will have a value when n = 1.

similarly, all the other terms will have the values given when we substitute their respective n values into the explicit formula or fibonacci sequence.

thus, check if the 1st term is 19 by using option 2

an = 19 + (n-1)(-5)

an = 19 + (n-1)(-5) ....n = 1

an = 19 + (n-1)(-5) ....n = 1 a1 = 19 + (1-1)(-5) = 19 + 0 = 19. so it's accurate so far.

next, check a2 where n = 2.

a2 = 19 + (2-1)(-5) = 19 - 5 = 14. ....

n = 3

a3 = 19 + (3-1)(-5) = 19 - 10 = 9.

hence the conclusion from this pattern.