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Andru [333]
3 years ago
15

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

Mathematics
2 answers:
koban [17]3 years ago
8 0

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

^{a}n = ^{a}1 (n - 1)d

In the formula, the <em>n </em>represents what term we want to find.

Since we want to find the 52nd term, we plug 52 in for <em>n</em>.

Then, ^{a}1 represents our first term in the sequence which is -3.

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

So we have ^{a}52 = -3+ (52 - 1)(15).

Now just simplify from here.

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

^{a} 52 = -3 + (51)(15).

Now, multiply before we add.

^{a}52 = -3 + 765.

Now just add to get ^{a}52 = 762.

Vika [28.1K]3 years ago
7 0

Answer:

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

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