arithmetic

Question

The fourth, fifth and sixth terms of a geometric sequence are
x - 4; x + 2 and 3x + 1
respectively. Determine:
(a) the possible values for x:
(b) the value for the first term in the sequence if x > 0 (i.e. x is positive).
3.2 The first term of an arithmetic sequence is 10 and the sixth term is 85. Find the first three
terms of the sequence. 

Answer 1

Hi Nono,

 

Maybe I'm being a little slow, but I can't quite read the first problem.  There are some weird characters that I'm having trouble figuring out what they mean, so maybe a quick re-post would help us?  Or, I'm not understanding what you've typed, which is totally possible.

 

Either way, maybe I can give a hint or two and see if it helps you, even without quite knowing the question.

 

- They've given you three consecutive terms in a geometric sequence.  If I take the fifth term and divide it by the fourth term, what's that thing called?

- How about if I take the sixth term and divide it by the fifth term?

- Can I use something about those two fractions to write an equation with just x's in it?

 

So, maybe that'll get you started.

 

As for 3.2, here are some hints:

 

- What is the formula for the nth term of an arithmetic sequence?  a_n= ...

- In that formula, what have they given you, and what are you trying to solve for?

- Once you've solved that, can you use what you know to figure out the first three terms of the sequence?

 

Hope that helps, but let us know if we need to take it a bit further.

 

-- Michael