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Find the nth term
4, 1, -2,-5, ... A32 ​

Sagot :

Wynliviaidn

Answer and step-by-step explanation:

To find the nth term of the given sequence, let's determine first what kind of sequence it is.

If it is an arithmetic sequence, let's find the common difference by subtracting a term by the previous term.

1 - 4 = -3

-2 - 1 = -3

-5 - (-2) = -3

The differences are all the same. Therefore, there is a common difference which is -3 and it is an arithmetic sequence.

Then let's find the nth term of the given sequence by using the formula for an arithmetic sequence:

An = A1 + (n - 1)d

where

An is the nth term,

A1 is the first term,

n is the number of terms, and

d is the common difference.

Let's substitute the given values to the formula.

An = A32

A1 = 4

n = 32

d = -3

A32 = 4 + (32 - 1)(-3)

A32 = 4 + (31)(-3)

A32 = 4 - 93

A32 = -89

Therefore, the 32nd term is -89.

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