In a certain sequence of numbers, each term after the first term is 3 times the preceding term. .. cont..?

Question

In a certain sequence of numbers, each term after the first term is 3 times the preceding term. If a and b are two terms in this swquence and if a / b is 27, how many terms are there between a and b, not including a and b?

In the right triangle ABC above, y/3=3/x + y. What is the value of y?

Right Triangle ( Hypotenuse facing the bottom.) (Base is 3 on the right)(Height is 4 on the left) ( Right angle on the top is making a altitude to the bottom making a point D and a right angel to the left.) Now There should be 2 triangles connecting to each other first one on the left is ABD 2nd is BDC.

So far im guessing that triangel BDC should be a right triangel as well

I mean triangle BDC should be a right triangle

Length BC is 3.
Length of AB is 4

Answer 1

Follow the reasoning of answer 1. terms are 3x, 9x, 27x, 81x etc As 3x/81x = 27, 9x and 27x are between these terms ie two terms.

If y/3 = 3/x + y (if that is what you mean and the x+y is not bracketed) the following applies:
multiply bs by 3
y = 9/x + y This is an impossible expression as 9/x = 0
y = 9/(x + y) is different.
Multiply bs by (x + y)
y(x + y) = 9 as I don't have the diag above you will have to take it from here.

Can't understand this one.

Answer 2

In a certain sequence of numbers, each term after the first term is 3 times the preceding term. If a and b are two terms in this swquence and if a / b is 27, how many terms are there between a and b, not including a and b?

Terms after a are 3a, 9a, 27a so there are TWO terms between a and b