Write an explicit formula for the sequence -13 , -6 , 1 , 8

Difference is 7

but here's the test answers too
1. C. 5,9,13,17,21
2. D. a1=14,an=an-1-4
3. C. an=-13+7(n-1)
4. D. 3.1 ft
5. D. an=22n
6. D. no
7. D. -24
8. B. 30
9. B. yes;3/4
10. C. 1/4096
11. B. -195 (its a typo, its supposed to be 195, but its listed as negative)
12. C. 450
13. A. 5 n-1 (-2.2+8.8n)
14. C. 752
15. D. 135
16. B. 3
17. D. 22 124/125 ft
18. C. It diverses; it does not have a sum

Good luck Compa~

Those aren't even close to the answers for the unit test lmao

No help ms sue

1. C 1,5,9,13,17

2. D a1=14,an=an-1-4
3. C an=-13+7(n-1)
4. B 4.1 feet
5. B an=24n
6. B no
7. D -24
8. B 30
9. C yes;2/3
10. C 1/4096
11. B -195
12. B 1350
13. D 5 n=1 (-4.4+6.6n)
14. A 783
15. C 80
16. A 4
17. D 22 124/125 feet
18. C it diverges; it does not have a sum

These answers are correct. The previous ones were incorrect.

To find an explicit formula for a sequence, we need to determine the pattern or rule that defines how each term is related to the previous term(s).

Looking at the given sequence: -13, -6, 1, 8, we can observe an increasing pattern. Each term is obtained by adding 7 to the previous term.

To express this pattern algebraically, we can say that the nth term (where n represents the position of the term) is given by:

a_n = a_1 + (n-1)d

In this formula, a_n is the nth term, a_1 is the first term, and d is the common difference between consecutive terms.

Let's substitute the given values into the formula:

a_1 = -13 (first term)
d = 7 (common difference)

a_n = -13 + (n-1)*7

Therefore, the explicit formula for the given sequence is:

a_n = -13 + 7(n-1)

What is the difference between each of those numbers?