Find the next three terms of the following sequence:
16,8,4, 2, 1

, ,

Step-by-step explanation:

There is a common ratio between consecutive terms in the sequence, that is

r = 8 ÷ 16 = 4 ÷ 8 = 2 ÷ 4 = 1 ÷ 2 =

Thus any term can be found by multiplying the previous term by

a₆ = × a₅ = × 1 =

a₇ = × a₆ = × =

a₈ = × a₇ = × =

1.3 million hoops i believe

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)