1: write a function rule to represent the sequence.
0.3, 0.9, 1.5, 2.1,

a. a(n) = 0.6+(m-1)0.3
b. a(n) = 0.6- (n)0.3
c. a(n) = 0.3+(n-1)0.6
d. a(n) = 0.3+(n+1)0.6

2: write a function rule to represent the sequence.
47, 32, 17, 2,

a. a(n) = 47+ (n-1)15
b. a(n) = 47+ (n-)
c. a(n) = 47+ (n-)
d. a(n) = 32+ (n-1)15

The correct answers are:

C) a(n) = 0.3+(n-1)0.6 ; and

C) a(n) = 47+ (n-1)(-15)

Explanation:

#1) This is an arithmetic sequence, since we are adding the same value to each term to find the next term. We add 0.6 each time, so this is the common difference. The first term is 0.3. This goes in the formula

#2) This is also an arithmetic sequence. This time, we add -15. The first term of this one is 47. This gives us:

hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)