Find the 4th term in the sequence with the following definition:
Please help!!

234

Step-by-step explanation:

Using the recursive formula and a₁ = 3, then

a₂ = 4a₁ + 2 = 4(3) + 2 = 12 + 2 = 14

a₃ = 4a₂ + 2 = 4(14) + 2 = 56 + 2 = 58

a₄ = 4a₃ + 2 = 4(58) + 2 = 232 + 2 = 234

Thus the 4 th term is 234

a1= 3

a2 = 4a(2-1)+2

= 4a1 +2

= 4( 3)+ 2 = 14

a3= 4a(3-1) +2

= 4a2 +2

= 4(14)+2

= 56+2 = 58

a4= 4a(4-1)+2

= 4a3 +2

= 4( 58) + 2

= 232+2= 234

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

9 sandwiches per hour

step-by-step explanation:

when we have a rate, we want a 1 in the denominator

27/3 = 9

27 sandwiches/ 3 hours = 9 sandwiches/hour