Question

What is the 100th term of the sequence 7, 4, 1, -2 ... PLEASE HELP!!!

A. 290
B. 304
C. -304
D. -290

Answer 1

Explanation:

Remark

What you want is the last term in an arithmetic sequence; n = 100.

Formula

L = a + (n - 1)*d

Givens

a = 7

d = - 3

n = 100

L = ?

Solution

L = 7 + (100 - 1)(-3) Remove the brackets

L = 7 + 99 * -3 Combine

L = 7 + - 297

L = -290

Answer

L = - 290

Answer 2

Option D,
`-290`

Explanation:

Step 1: Determine the equation

We know that the initial value is 7 so that will be our starting point in the equation. We can also see that every time we go to the next number, our number has 3 subtracted from it. Therefore, we can use n-1 which will help us determine how much we need to subtract from the initial number. Here is the recursive equation

`T = 7 - 3(n - 1)`

Step 2: Determine the 100th term of the sequence

`T = 7 - 3(100 - 1)`

`T = 7 - 3(99)`

`T = 7 - 297`

`T = -290`

Answer: Option D,
`-290`