Question

What is the explicit formula for this sequence?

-8,-3, 2, 7, ...
O A. an = 12 + (n - 1)5
O B. an = 5+(n-1)(-8)
O C. an=-8+ (n - 115
O D. an= -8+ (n - 1)(-5)

Answer 1

`\text{C. }a_n=-8+(n-1)5`

Explanation:

The explicit formula for an arithmetic sequence is given by
`a_n=a_1+(n-1)d`, where
`a_n` is the
`n`th,
`a_1` is the first them of the sequence, and
`d` is the common difference.

In the given sequence -8, -3, 2, 7, we can see that we're adding 5 to each term. Therefore, the common different is positive five (+5). We can also identify the first term is -8. Therefore, we have:

• 
  `a_1=-8`
• 
  `d=5`

Thus, the explicit formula for this sequence is:

`\boxed{a_n=-8+(n-1)5}`