The general term of an arithmetic sequence is tn = 32 + 3n, where n ∈n and n ≥ 1. the sequence is
a) 32, 35, 38, 41, 44,
b) 32, 96, 288, 864, 2592,
c) 34, 39, 44, 49, 54,
d) 35, 38, 41, 44, 47,

D) 35, 38, 41, 44, 47, 50, ...

Step-by-step explanation:

tₙ  = 32 + 3n; n ∈ N, n ≥ 1

t₁  = 32 + 3(1) = 32 +  3 = 35

t₂ = 32 + 3(2) = 32 +  6 = 38

t₃ = 32 + 3(3) = 32 +  9 = 41

t₄ = 32 + 3(4) = 32 + 12 = 44

t₅ = 32 + 3(5) = 32 + 15 = 47

t₆ = 32 + 3(6) = 32 + 18 = 50

The sequence starts at t₁ = 35 and each term is 3 units greater than the preceding term.

The sequence is 35, 38, 41, 44, 47, 50, ...

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