Question

3. Consider the sequence,-8, -5, -2, 1, ...

Answer 1

Answer:

a) $a_n=3\,n-11$

b) $a_{20}=49$

c) term number 17 is the one that gives a value of 40

Step-by-step explanation:

a)

The sequence seems to be arithmetic, and with common difference d = 3.

Notice that when you add 3 units to the first term (-80, you get :

-8 + 3 = -5

and then -5 + 3 = -2 which is the third term.

Then, we can use the general form for the nth term of an arithmetic sequence to find its simplified form:

$a_n=a_1+(n-1)\,d$

That in our case would give:

$a_n=-8+(n-1)\,(3)\\a_n=-8+3\,n-3\\a_n=3n-11$

b)

Therefore, the term number 20 can be calculated from it:

$a_{20}=3\,(20)-11=60-11=49$

c) in order to find which term renders 20, we use the general form we found in step a):

$a_n=3\,n-11\\40=3\,n-11\\40+11=3\,n\\51=3\,n\\n=\frac{51}{3} =17$

so term number 17 is the one that renders a value of 40