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

762

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