If t8 = 4 and t12 = −2, find the first three terms of the arithmetic sequence.

The first three terms of the arithmetic sequence are 29/2, 13, 23/2.

Given

The value of = 4 and = −2.

The difference between two consecutive terms is constant is called an arithmetic sequence.

The general form of the arithmetic sequence.

Where, is the first term and d is the common difference of the arithmetic sequence.

The 8th term of the sequence is;

The 12th term of the sequence is;

Subtract both the equations;

The common difference between the terms is -3/2.

Then,

The first term of the sequence is;

The first term of the sequence is 29/2.

Therefore,

The second term of the sequence is;

And a third of the sequence is;

Hence, the first three terms of the arithmetic sequence are 29/2, 13, 23/2.

To know more about arithmetic sequence click the link given below.

link

  14.5, 13, 11.5

Step-by-step explanation:

The general term (an) of an arithmetic sequence with first term a1 and common difference d is ...

  an = a1 + d(n-1)

Then the 8th term is ...

  a8 = a1 + d(8-1)

and the 12th term is ...

  a12 = a1 + d(12-1)

So, the difference between these terms is ...

  a12 -a8 = (a1 +11d) -(a1 +7d) = 4d

  = (-2-4) = -6 . . . . . substituting values for a12 and a8

Then the common difference is

... d = -6/4 = -3/2

Using this, we can find a1 from a8.

  4 = a1 +7·(-3/2) = a1 - 10.5

  14.5 = a1 . . . . . . . add 10.5 to both sides of the equation

This is the first term. The second is this value with the common difference added:

  14.5 + (-1.5) = 13

The third term is this with the common difference added:

  13 + (-1.5) = 11.5

In summary, the first three terms are ...

  14.5, 13, 11.5

add an image !

step-by-step explanation:

all it means is function 3