Inorder to fix for a nth hatchet in an arithmetic sequence, we usage the formulawritten as:an = a1 + (n-1)dwhere one is the nth term, a1 is the an initial valuein the sequence, n is the term position and also d is the common difference.First, we need to calculate for d native the givenvalues above. A1 = -31 and also a17 = -119an = a1 + (n-1)d-119 = -31 + (9-1)dd = -11The 32nd ax is calculated as follows:a32 = a1 + (n-1)da32= -31 + (32-1)(-11)a32 = -372  =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 by According 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 and We 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 and Calculate 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,  a 32 = -171

Step-by-step explanation:

a.-171

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