Consider the sequence: 3, 8, 13, 18, 23, recursive formula for this sequence is: an = an-1 + 5in a complete sentence, explain what an and an-1 represent in the formula. then find a8 . what do you need to know in order to find a8 ?

see the explanation

Step-by-step explanation:

we know that

In an Arithmetic Sequence the difference between one term and the next is a constant called the common difference

we have

Let

------>

------>

------>

------>

so

the common difference between consecutive terms is equal to 5

we can rewrite the formula as

-----> given formula

For n > 1

where

an is the term that you want to find (position n)

a(n-1) is the known term position (n-1)

Find a_8

For n=8

I need to know a_7

or

we know that

The general formula for arithmetic sequence is equal to

where

an is the term that you want to find (position n)

a_1 is the first term

d is the common difference

n is the number of terms

we have

substitute

so

For n=8

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

if x = 1, then the answer is 3.5