Which sequences could be described by the recursive definition latex: a_{n+1}=3\cdot a_n-1a n + 1 = 3 ⋅ a n − 1
group of answer choices

2, 5, 14, 41,

2, 5, 8, 11,

2, 3, 5, 11, 29,

2,6,18,54,

Step-by-step explanation:

The given expression is:

To find the right sequence, we have to find the value for , , , and , which are presented in the following operations, also we know that the first term is 2, we can begin from there:

As you can see, the given expression represents a sequence where the next term is the triple than the term before.

As a result, we found the sequence 2, 6, 18, 54, 162...

Therefore the right answer is the last choice.

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