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A sequence of numbers a1, a2, a3, . . . is defined as follows: a1 = 3, a2 = 5, and every term in the sequence after a2 is the product of all terms in the sequence preceding it, e.g., a3 = (a1)(a2) and a4 = (a1)(a2)(a3). If an = t and n > 2, what is the value of an+2 in terms of t?

A sequence of numbers \( a_1, a_2, a_3, \dots \) is defined as follows: \( a_1 = 3 \), \( a_2 = 5 \), and every term in the sequence after \( a_2 \) is the product of all terms in the sequence preceding it, e.g., \( a_3 = (a_1)(a_2) \) and \( a_4 = (a_1)(a_2)(a_3) \). If \( a_n = t \) and \( n > 2 \), what is the value of \( a_{n+2} \) in terms of t?

A. \( 4t \)

B. \( t^2 \)

C. \( t^3 \)

D. \( t^4 \)

E. \( t^8 \)

Show the answer

Correct Answer: D

You’ll find tons of practice questions, explanations for GMAT Official Guide questions, and strategies on our GMAT Question of the Day page.

Here are a few other extra challenging GMAT questions with in depth explanations:

Here’s a tough function question from the GMAT Prep tests 1 and 2:

For which of the following functions is f(a+b) = f(b) + f(a) for all positive numbers a and b?

And a very challenging word problem from the Official Guide. Almost no-one gets this one on the first try but there is a somewhat simple way through it:

Last Sunday a certain store sold copies of Newspaper A for $1.00 each and copies of Newspaper B for $1.25 each, and the store sold no other newspapers that day. If r percent of the store’s revenues from newspaper sales was from Newspaper A and if p percent of the newspapers that the store sold were copies of newspaper A, which of the following expresses r in terms of p?

Tanya’s letters from the GMAT Prep tests. This one often gets GMAT tutoring students caught up in a tangled net. With combinatorics it’s important to stay practical. We’ll take a look at how to do that in the explanation:

Tanya prepared 4 different letters to be sent to 4 different addresses. For each letter, she prepared an envelope with its correct address. If the 4 letters are to be put into the 4 envelopes at random, what is the probability that only 1 letter will be put into the envelope with its correct address?

Here’s an exponents puzzle that comes up a lot in GMAT tutoring sessions:

If n is a positive integer and n^2 is divisible by 72, then the largest positive integer that must divide n is

This is one of the most difficult questions in the GMAT universe. That said, there is a simple way to solve it that relies on a fundamental divisibility rule every GMAT studier should know:

For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100) +1, then p is?