3. How much information does one need to determine an arithmetic sequence? That is, if a person tells you that she is thinking of an arithmetic sequence, how
many, or which, terms must be revealed such that you will be able to create the
function that generates the terms of the sequence?

70

step-by-step explanation:

80 the answer is 80

step-by-step explanation:

hello from mrbilldoesmath!

answer:

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

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

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

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb