Question

Find the three arithmetic means in this sequence 2,_,_,_,-18

Answer 1

2, -3, -8, -13, -18.

Explanation:

In order to find the three arithmetic means in the given sequence, we first need to determine the common difference between consecutive terms.

In an arithmetic sequence, the common difference (d) is constant, which means the difference between any two consecutive terms remains the same.

Let's calculate the common difference (d) using the given information:

First term (a) = 2

Fifth term (t5) = -18

The formula for the nth term of an arithmetic sequence is:

`\boxed{\sf An = a + (n-1) * d}`

For the fifth term (n = 5), we have:

`\sf -18 = 2 + (5-1) * d`

`\sf -18 = 2 + 4d`

Now, we can solve for the common difference (d):

`\sf -18 - 2 = 4d`

`\sf -20 = 4d`

`\sf d = (-20)/(4)`

d = -5

Therefore, common difference = -5.

Now.

2nd term = 2+(2-1)( -5)=2-5=-3

3rd term = 2+(3-1)(-5)=2+2*(-5)=2-10=-8

4th term = 2+(4-1)(-5)= 2+3*(-5)=2-15=-13

So, the three arithmetic means in the given sequence are: -3, -8, and -13.

The complete sequence is: 2, -3, -8, -13, -18.