GRE Math question--Sequence of numbers

kateglynn · #1 $Old$ April 19th, 2008, 06:50 PM

Just took a practice GRE, and was STUMPED by this question. Please help!

Let A1, A2, A3...An be a sequence of positive integers where A1=1 and A(n+1)=(An)+4. What represents the nth term?

The answer is 4n-3, but I have NO idea how to get there!

Soroban · #2 $Old$ April 19th, 2008, 07:27 PM

Hello, kateglynn!

Quote:

Let $A_1, A_2, A_3, \hdots A_n$ be a sequence of positive integers
. . where $A_1=1\,\text{ and }\,A_{n+1} \,=\, A_n +4$
What represents the $n^{th}$ term?

Look at the recurrence: . $A_{n+1} \;=\;A_n + 4$

It says: Each term is 4 more than the preceding term . . . right?

The sequence starts with 1 and "goes up by 4's".

So we have: . $1, 5, 9, 13, 17, \hdots$

Can you create a function that generates those numbers for $n = 1,2,3,\hdots$ ?

Jhevon · #3 $Old$ April 19th, 2008, 07:28 PM

Quote:

Originally Posted by kateglynn $View Post$

Just took a practice GRE, and was STUMPED by this question. Please help!

Let A1, A2, A3...An be a sequence of positive integers where A1=1 and A(n+1)=(An)+4. What represents the nth term?

The answer is 4n-3, but I have NO idea how to get there!

recall what an arithmetic series is. they described an arithmetic series here. can you figure out the answer now?

awkward · #4 $Old$ April 19th, 2008, 07:51 PM

Quote:

Originally Posted by kateglynn $View Post$

Just took a practice GRE, and was STUMPED by this question. Please help!

Let A1, A2, A3...An be a sequence of positive integers where A1=1 and A(n+1)=(An)+4. What represents the nth term?

The answer is 4n-3, but I have NO idea how to get there!

Kateglynn,

Could this be a multiple choice question in which 4n-3 is one of the choices?

If so, the easy way to answer the question it is to just check to see if 4n-3 satisfies the recurrence:

Is A(1) = 1?
4(1) -3 = 1 CHECK!

Is A(n+1) = A(n) + 4?
4(n+1) = 4n + 4 CHECK!

Just a little test-taking strategy...
jw