Question

-2, ___, ___, -16 …

If this sequence is arithmetic then it has a common ________
of ______.

Show WORK here:

Answer 1

-4,-8
It has a common ratio of 2

Answer 2

`-2, \boxed{-(20)/(3)}\:,\boxed{-(34)/(3)}\:, -16`

`\textsf{If this sequence is arithmetic then it has a common $\boxed{\sf difference}$ of $\boxed{-(14)/(3)}$\:.}`

Explanation:

An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant.

The given terms of the sequence are:

`a_1 = -2`

`a_4 = -16`

To find the common difference (d), we can divide the difference of the given terms by the difference of their positions:

`d=(a_4-a_1)/(4-1)=(-16-(-2))/(4-1)=-(14)/(3)`

To find terms 2 and 3, add the common difference (d) to the previous term:

`a_2=a_1+\left(-(14)/(3)\right)=-2-(14)/(3)=-(20)/(3)`

`a_3=a_2+\left(-(14)/(3)\right)=-(20)/(3)-(14)/(3)=-(34)/(3)`

`a_4=a_3+\left(-(14)/(3)\right)=-(34)/(3)-(14)/(3)=-(48)/(3)=-16`

Therefore, the common difference of the given arithmetic sequence is -14/3, and the second and third terms are -20/3 and -34/3 respectively.