Question

What is the 30th term of the arithmetic sequence?

15, 11, 7, 3, -1.....

A.) 131
B.) -5
C.) -101
D.) -105

Answer 1

The correct answer is:

C.) -101

Answer 2

C.
`a_3_0=-101`

Explanation:

We have the arithmetic sequence 15,11,7,3,-1,...

Where,

`a_1=15,\\a_2=11,\\a_3=7,\\a_4=3,\\a_5=-1,...`

You can see that the common difference d=(-4), or if you couldn't see the common difference you can calculate it with the formula:

`d=a_n_+_1-a_n`

Then,

`d=a_2-a_1\\d=11-15\\d=(-4)`

Now to find the 30th term of the arithmetic sequence we can use the following formula:

`a_n=a_1+(n-1).d`

Replacing n=30,
`a_1=15` and d=(-4):

`a_n=a_1+(n-1).d\\a_3_0=15+(30-1)(-4)\\a_3_0=15-29.4\\a_3_0=15-116\\a_3_0=-101`

Then the correct option is C.
`a_3_0=-101`