Respuesta :

drwnd
firstly we have to find d:
[tex]d = \frac{a_{n}-a_{m}}{n-m} [/tex]  ⇒
[tex]d = \frac{-120-(-32)}{9-1} = \frac{-88}{8} = -11[/tex]
now, when we know d, we can find the 32nd term by using a following formula:
[tex]a_{n}=a_{1}+(n-1)*d[/tex]
[tex]a_{32} =-32+31*(-11) = -32-341 = -373[/tex]
the answer is [tex]a_{32} = -373[/tex]

Answer:

-373

Step-by-step explanation:

A

n

=

A

1

+

d

(

n

−

1

)

A

1

=

−

32

A

9

=

−

120

⇒

A

9

=

−

32

+

d

(

9

−

1

)

⇒

−

120

=

−

32

+

d

(

8

)

⇒

−

88

=

8

d

⇒

d

=

−

11

A

32

=

−

32

+

(

−

11

)

(

32

−

1

)

⇒

A

32

=

−

32

+

(

−

11

)

(

31

)

⇒

A

32

=

−

32

+

−

341

⇒

A

32

=

−

373