## GucciDoTheDishes one year ago ** will medal and fan What are the explicit equation and domain for an arithmetic sequence with a first term of 5 and a second term of 2?

1. guccidothedishes

n=5−2(n−1);allintegerswheren$≥1 an=5−2(n−1);allintegerswheren\[≥0 an=5−3(n−1);allintegerswheren\[≥1 an=5−3(n−1);allintegerswheren\[≥0 2. guccidothedishes @liljj1421 ?? 3. guccidothedishes @Michele_Laino 4. Michele_Laino hint: we can write this: \[\Large \begin{gathered} {a_2} = {a_1} + d \hfill \\ 2 = 5 + d \hfill \\ \end{gathered}$ where d is the sequence constant

5. Michele_Laino

what si d?

6. Michele_Laino

after that the general formula, for the n-th term is: $\Large {a_n} = {a_1} + \left( {n - 1} \right)d$ where a_1=5

7. guccidothedishes

how do I get d ?

8. Michele_Laino

it is simple, from the second equation, I can write: $d = 2 - 5 = ...?$

9. guccidothedishes

so D=3 ?

10. Michele_Laino

no, d=-3

11. guccidothedishes

12. guccidothedishes

but how do I determine the second part of the answer?

13. Michele_Laino

yes! furthermore, please keep in mind that we start to count from n=1

14. guccidothedishes

15. Michele_Laino

yes! That's right! since if n=1, we get: ${a_1} = {a_1} + \left( {1 - 1} \right)d = 5 + 0 \times \left( { - 3} \right) = 5$

16. guccidothedishes

Thank you so much :)

17. Michele_Laino

:)