Question

Which of the following best describes the set of numbers?

-1, 2, -4, 8, ...

Infinite arithmetic series
Finite geometric series
Infinite geometric series
Infinite alternating sequence

Answer 1

This is a
Infinite alternating sequence

Since it can go on forever and every other number is a negative one.

Answer 2

Infinite alternating sequence

Explanation:

As we know that series is basically sum of sequence, so, the given set of numbers is not an infinite arithmetic series, finite geometric series and an infinite geometric series as it is just a sequence of numbers

Now, we need to check if
`-1,2,-4,8...` is an infinite alternating sequence or not .

An infinite alternating sequence is basically of form
`(-1)^(n+1)2^n`

If we take
`a_n=2^n`

For n=0 , we get
`a_0=2^0=1`

For n=1 , we get
`a_1=2^1=2`

For n=2 , we get
`a_2=2^2=4`

For n=3 , we get
`a_3=2^3=8` and so on

So, we get sequence as
`\left ( -1 \right )^(1)2^0\,,\,\left ( -1 \right )^(2)2^(1)\,,\,\left ( -1 \right )^(3)2^(2)\,,\,\left ( -1 \right )^(4)2^(3)\,...`

i.e
`-1,2,-4,8...`