Bunuel wrote:
The sequence \(a_1\), \(a_2\), \(a_3\), ... , \(a_n\), ... is such that \(a_n=\frac{a_{n-1}+a_{n-2}}{2}\) for all \(n\geq{3}\). If \(a_3 = 4\) and \(a_5 = 20\), what is the value of \(a_6\) ?
(A) 12
(B) 16
(C) 20
(D) 24
(E) 28
Please note: this question in the 2017 version of the
OG (page 20, #3, Quant Diagnostic Test) contains a typo. It should say \(a_n=\frac{a_{n-1}+a_{n-2}}{2}\) for all \(n\geq{3}\), but instead it says \(a_n=\frac{a_{n+1}+a_{n-2}}{2}\) for all \(n\geq{3}\). The answer explanation on page 46, however, lists the correct formula.
Yes, even the GMAC makes mistakes!
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My name is Brian McElroy, founder of McElroy Tutoring (https://www.mcelroytutoring.com). I'm a 42 year-old Providence, RI native, and I live with my wife, our three daughters, and our two dogs in beautiful Colorado Springs, Colorado. Since graduating from Harvard with honors in the spring of 2002, I’ve worked full-time as a private test-prep tutor, essay editor, author, and admissions consultant.
I’ve taken the real GMAT 6 times — including the GMAT online — and have scored in the 700s each time, with personal bests of 770/800 composite, Quant 50/51, Verbal 48/51, IR 8 (2 times), and AWA 6 (4 times), with 3 consecutive 99% scores on Verbal. More importantly, however, I’ve coached hundreds of aspiring MBA students to significantly better GMAT scores over the last two decades, including scores as high as 720 (94%), 740 (97%), 760 (99%), 770, 780, and even the elusive perfect 800, with an average score improvement of over 120 points.
I've also scored a verified perfect 340 on the GRE, and 179 (99%) on the LSAT.