Find the 20th term of the arithmetic sequence

First we must look at the sequence 15,9,3,-3...

You can see that the value is decreasing by 6 every term. Because the rate is drawing at a constant rate the sequence must be linear, meaning that the slope is -6.

If we look at the general function of a line in slope intercept form:

[tex]y = mx + b[/tex]
where m is the slope and b is the y intercept. The trick to find the y intercept is to go backwards, in other words what was the previous term? 15+6=21. Therefore, m=-6 and b=21 and thus,

[tex]y = - 6 x+ 21[/tex]
Since we want to know the value of y even x=20 we obtain:

[tex]y = - 6(20) + 21 \\ \\ y = - 99[/tex]

Phoca Phoca · Answer 2 · 2018-12-31T06:05:48+01:00

Answer:

-99

Step-by-step explanation:

Given :

Arithmetic sequence : 15 , 9 ,3 , -3 , ........

To Find : 20th term .

Solution :

Formula of nth term in Arithmetic mean : [tex]a_{n} = a+(n-1)*d[/tex] ---(A)

where

a = first term of sequence

n = term position

d = common difference

[tex]a_{n}[/tex] = the term you want to find

Thus in the given sequence:

a = 15 ( first term )

n = 20 th term ( given )

d = 9-15 = 3-9 = -6(common difference)

Putting values in (A)

⇒[tex]a_{20} = 15+(20-1)*(-6)[/tex]

[tex]a_{20} = 15-114[/tex]

[tex]a_{20} = -99[/tex]

Hence the 20th term is -99 i.e. option 1