A mathematician has devised a formula that produces a series of numbers s_1, s_2, . . . , s_x according to the principles $$s_1=2, s_2=2, s_3=2,$$ and for $$x \geq 4,\,\,s_x=2s_{x-1}+s_{x-2}.$$ Which of the following equals $$s_6=?$$
A. 30
B. 34
C. 37
D. 38
E. 40
The OA is B
Source: Princeton Review
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A mathematician has devised a formula that produces a series
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Hi All,
In this question, we're given the 'rules' for a particular sequence. We have the values of the first 3 terms and instructions for how to calculate each term afterwards (re: the 4th term is the sum of TWICE the term before it and the term '2 terms' before it - re: 2(3rd term) + 2nd term). We're asked for the value of the 6th term. In these of sequence questions, it can sometimes help to 'map out' what you know and determine as many values as you need to to answer the given question.
1st term = 2
2nd term = 2
3rd term = 2
4th term = (2)(2) + 2 = 6
5th term = (2)(6) + 2 = 14
6th term = (2)(14) + 6 = 34
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
In this question, we're given the 'rules' for a particular sequence. We have the values of the first 3 terms and instructions for how to calculate each term afterwards (re: the 4th term is the sum of TWICE the term before it and the term '2 terms' before it - re: 2(3rd term) + 2nd term). We're asked for the value of the 6th term. In these of sequence questions, it can sometimes help to 'map out' what you know and determine as many values as you need to to answer the given question.
1st term = 2
2nd term = 2
3rd term = 2
4th term = (2)(2) + 2 = 6
5th term = (2)(6) + 2 = 14
6th term = (2)(14) + 6 = 34
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
