Question

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

Answer 1

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

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

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, $^{a}1$ 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 $^{a}52 = -3+ (52 - 1)(15)$.

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 $^{a}52 = 762$.

Answer 2

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