=D

The correct alternative is (B) -172.

You are watching: What is the 32nd term of the arithmetic sequence where a1 = 15 and a13= −57?

Step-by-step explanation: we are provided to discover the 32nd hatchet of the arithmetic sequence whereby the first term and 13th hatchet are

We understand that

the n-th term of an arithmetic sequence with an initial term

and common distinction is given byAccording come the given information, we have

and

Therefore, the 32nd term will be

Thus, the 32nd ax is -172.

Option (B) is correct.

- 174

Step-by-step explanation:

The nth ax of one arithmetic sequence is provided as

Tn = a + (n - 1)d

where Tn is the nth term

a is the first term , n is the variety of term and also d is the common difference. Together such,

a13 = a + (13 - 1)d

= a + 12d

Given that a1 = 12 and a13 = -60

-60 = 12 + 12d

12d = -72

d = -6

Hence a32 i m sorry is the 32nd term

= 12 + (32 - 1)-6

= 12 + (-186)

= - 174

-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

Step-by-step explanation:

Given : the arithmetic succession where

andWe have to uncover the 32nd ax of the arithmetic sequence.

Since, the basic arithmetic succession having first term "a" and also common distinction "d" is provided by

Thus, because that the provided arithmetic sequence, us have,

very first term is

andCalculate the common difference by placing a = 13 in above, we have,

Solving because that d, we have,

Divide by 12 both side, we have,

Thus, the usual difference is -6.

For 32nd term, placed a = 13 , d = -6 and n = 32 in

We have,

Simplify, us have,

Answer from: JackMonhen

a 32 = -171

Step-by-step explanation:

a.-171

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