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505-555 (Easy)|   Sequences|      
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Bunuel
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A mathematician has devised a formula that produces a series of number 13 Jun 2018, 12:16
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15% (low)

Question Stats:

81% (01:39) correct 19% (01:47) wrong based on 158 sessions

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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 \(x \geq 4\), \(s_x = 2*s_{x-1} + s_{x-2}\) . Which of the following equals \(s_6=\) ?

A) 30

B) 34

C) 37

D) 38

E) 40
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B
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A mathematician has devised a formula that produces a series of number 13 Jun 2018, 13:54
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Bunuel
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 \(x \geq 4\), \(s_x = 2*s_{x-1} + s_{x-2}\) . Which of the following equals \(s_6=\) ?

A) 30

B) 34

C) 37

D) 38

E) 40
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Using the formula \(s_x = 2*s_{x-1} + s_{x-2}\), we can come up with the values of \(s_4, s_5,\) and \(s_6\)

\(s_4 = 2*s_{3} + s_{2}\) | \(s_5 = 2*s_{4} + s_{3}\) | \(s_6 = 2*s_{5} + s_{4}\)

\(s_6 = 2*s_{5} + s_{4} = 2*(2*s_{4} + s_{3}) + 2*s_{3} + s_{2} = 2*(2*(2*s_{3} + s_{2}) + s_{3}) + 2*s_{3} + s_{2}\)

Therefore, \(s_6 = 2*(2*(2*2 + 2) + 2) + 2*2 + 2 = 2*(2*(6) + 2) + 6 = 2*(12 + 2) + 6\) = 34(Option B)
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A mathematician has devised a formula that produces a series of number 13 Jun 2018, 14:11
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B
\(s_4 = 2 s_3 + s_2 = 6\)
\(s_5 = 2 s_4 + s_3 = 14\)
\(s_6 = 2 s_5 + s_4 = 34\)
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A mathematician has devised a formula that produces a series of number 13 Jun 2018, 22:34
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Solution



Given:
    • In the series, \(S_1 = S_2 = S_3 = 2\)
    • For x ≥ 4, \(S_x = 2* S_{x-1} + S_{x-2}\)

To find:
    • The value of \(S_6\)

Approach and Working:
For x ≥ 4, we can find the values of Sx using the given relation \(S_x = 2* S_{x-1} + S_{x-2}\)
    • \(S_4 = 2*S_3 + S_2 = 2*2 + 2 = 6\)
    • \(S_5 = 2*S_4 + S_3 = 2*6 + 2 = 14\)
    • \(S_6 = 2*S_5 + S_4 = 2*14 + 6 = 34\)

Hence, the correct answer is option B.

Answer: B
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A mathematician has devised a formula that produces a series of number 13 Jun 2018, 22:39
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Answer is B. If you work your way through the formula given, it will lead to 34.
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A mathematician has devised a formula that produces a series of number 17 Jun 2018, 19:42
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Bunuel
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 \(x \geq 4\), \(s_x = 2*s_{x-1} + s_{x-2}\) . Which of the following equals \(s_6=\) ?

A) 30

B) 34

C) 37

D) 38

E) 40
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s(4) = 2 x s(3) + s(2) = 2 x 2 + 2 = 6

s(5) = 2 x s(4) + s(3) = 2 x 6 + 2 = 14

s(6) = 2 x s(5) + s(4) = 2 x 14 + 6 = 34

Answer: B
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A mathematician has devised a formula that produces a series of number 15 Dec 2018, 19:26
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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:
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B


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A mathematician has devised a formula that produces a series of number 17 Feb 2023, 05:34
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