Find an equation for the nth term of the arithmetic sequence.

a19 = -92, a20 = 6

Question

Find an equation for the nth term of the arithmetic sequence.

a19 = -92, a20 = 6

hang254 · Answer

@Nurali

mathstudent55 · Answer

What is the common difference?

irishboy123 · Answer

arithmetic series goes :  a + (a+d) + (a + 2d) + ......

***the difference between consecutive terms is d.

***the nth term is a + (n-1), so the 20th term is a + 19 d



you now have everything you need to nail this.

hang254 · Answer

86

mathstudent55 · Answer

$a_1 = a_1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = a_1 + 0d$
$a_2 = a_1 + 1d~~~~~~~~~~~~~~~~~~~~~~~~~~ = a_1 + 1d$
$a_3 = a_2 + d = a_1 + d + d ~~~~~= a_1 + 2d$
$a_4 = a_2 + d = a_1 + 2d + d ~~~= a_1 + 3d$
This suggests an nth term:
$a_n = a_1 + (n - 1)d$

mathstudent55 · Answer

You have two consecutive terms, a19 and a20.
If you subtract a20 - a19, you will find d.
What is d?

mathstudent55 · Answer

@IrishBoy123 
You meant:
"***the nth term is a + (n-1)d, so the 20th term is a + 19 d"
                                             ^

irishboy123 · Answer

@mathstudent55  you are eagle eyed!

hang254 · Answer

d = 1

$$a _{n}=-1856+98(n-1)$$

hang254 · Answer

@mathstudent55

mathstudent55 · Answer

a20 - a19 = 98
d = 98
Now we know the common difference is 98.

mathstudent55 · Answer

$a_{19} = a_1 + 18d$
$a_19 = a_1 + 18 \times 98$
$-92 = a_1 + 1764$
$a_1 = -1856$

mathstudent55 · Answer

You are correct.

hang254 · Answer

Thank You !

mathstudent55 · Answer

You're welcome.