Write the first three terms in the following sequences. identify them as arithmetic or geometric
c. a(n + 1) = a(n) ÷ 10 for n ≥ 1 and a(1) = 10

10, 1, 0.1, 0.01

It is a geometric sequence

Step-by-step explanation:

A(n + 1) = A(n) ÷ 10  for  n ≥ 1  and  A(1) = 10

A(1+1) = A(2) = A(1) / 10 = 10 / 10 = 1

A(2+1) = A(3) = A(2) / 10 = 1 / 10 = 0.1

A(3+1) = A(4) = A(3) / 10 = 0.1 / 10 = 0.01

It corresponds to a geometric sequence, which is defined by its starting number a (10), the common factor r (0.1) and the number of terms S.

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