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MissPhiladelphia

For the answer to the question above asking the explicit equation and domain for an arithmetic sequence with the first term of 5 and the second term of 2? I think the answer for this is 5-2(n-1); all integers where n≥0. I hope this helps.

Answer:

\(a_n= 8-3n\) is the explicit equation, integers n>0

Step-by-step explanation:

an arithmetic sequence with a first term of 5 and a second term of 2

General formula for arithmetic sequence is \(a_n= a_1+(n-1)d\)

where a1 is the first term and d is the common difference

\(a_1=5\)

\(a_2=2\)

Difference between the terms = 2-5=-3

Difference d=-3

a1=5, d=-3, plug in all the values

\(a_n= 5+(n-1)(-3)\)

multiply -3 inside the parenthesis

\(a_n= 5-3n+3\), combine like terms

\(a_n= 8-3n\) is the explicit equation, n>0

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