Find the 52nd term of the arithmetic sequence -3, 12, 27, ...

762

Step-by-step explanation:

Notice that each new term is equal to the preceding term PLUS 15.  Thus, the common difference is 15 and the first term is -3.

The explicit equation for this sequence is

a(n) = -3 + 15(n - 1)

So the 52nd term is a(52) = -3 + 15(51) = 762

Start with your explicit formula which I have provided for you below.

In the formula, the n represents what term we want to find.

Since we want to find the 52nd term, we plug 52 in for n.

Then, represents our first term in the sequence which is -3.

Now, d is the difference between each of the terms and it's 15.

So we have .

Now just simplify from here.

First, apply order of operations (inside parentheses first).

.

Now, multiply before we add.

.

Now just add to get .

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step-by-step explanation: