Answer:

n=46

Step-by-step explanation:

The sequence given above is an arithmetic sequence.

First, we need to find the common difference d by using the equation

where is the first term and is the nth term.

Let n = 2, so = 7/3 or the second term and = 3

Substitute:

7/3 = 3 + (2-1) d

7/3 = 3 + 1d

(7/3) - 3 = (3 + 1d) -3 (Additive property of equality)

- 2/3 = d

Now that we know the common difference, we can now use the equation

to find the value of n, given that = -27

Substitue:

-27 = 3 + (n -1)(-2/3)

-27 = 3 - 2/3n + 2/3 (Distributive property)

2/3n = 3 + 2/3 + 27 (Additive property, here we add 2/3n and 27 on both sides)

2/3n = 92/3

n = 46 (Multiplicative inverse property in which we multiply both sides by 3/2)

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