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Indicate the general rule for the arithmetic sequence with a3 = -4 and a8 = -29.

2 Answers

4 votes

Answer:

a n = -6 + (n - 1)(5) is correct <3

Explanation:

User SilentSteel
by
8.1k points
6 votes
The general rule would be


a_n=6-5(n-1)

We first find the common difference, the value that is added every time to find the next term. This is the same as the slope; the formula for slope is

m=(y₂-y₁)/(x₂-x₁)

Letting x be the term number and y be the term value, we have
m=(-29--4)/(8-3) = (-29+4)/(8-3) = -25/5 = -5

Now we work backwards from a₃ to find a₁, the first term. We know that the common difference is -5; that means each time, the next term is found by subtracting 5. If we want to work backward we will add 5:
-4+5=1 for a₂
1+5=6 for a₁

Now we can write the general form:

a_n=6-5(n-1)
User Geekygeek
by
8.4k points

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