Question

** 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?

Answer 1

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

Answer 2

@liljj1421 ??

Answer 3

@Michele_Laino

Answer 4

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

Answer 5

what si d?

Answer 6

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

Answer 7

how do I get d ?

Answer 8

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

Answer 9

so D=3 ?

Answer 10

no, d=-3

Answer 11

okay so I can already eliminate 2 of the answer choices

Answer 12

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

Answer 13

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

Answer 14

So my answer is C

Answer 15

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

Answer 16

Thank you so much :)

Answer 17

:)