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If An+1=120 + (1/4)An for each positive integer n, and A1=150, which o

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If An+1=120 + (1/4)An for each positive integer n, and A1=150, which o  [#permalink]

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New post 27 Jun 2018, 01:02
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[GMAT math practice question]

If \(A_{n+1}=120 + (\frac{1}{4})A_n\) for each positive integer \(n\), and \(A_1=150\), which of these ranges of values includes \(A_{12}\)?

A. 110-120
B. 120-130
C. 130-140
D. 140-150
E. 150-160

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Re: If An+1=120 + (1/4)An for each positive integer n, and A1=150, which o  [#permalink]

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New post 27 Jun 2018, 02:19
1
MathRevolution wrote:
[GMAT math practice question]

If An+1=\(120 + (\frac{1}{4})\)An for each positive integer \(n\), and A1=150, which of these ranges of values includes A12?

A. 110-120
B. 120-130
C.130-140
D. 140-150
E. 150-160


\(A_2 = 120 + \frac{1}{4}A_1 = 120 + \frac{1}{4}*150 = 120 + 37.5 = 157.5\)
\(A_3 = 120 + \frac{1}{4}A_2 = 120 + \frac{1}{4}*157.5 ≈ 120 + 39 = 159\)
\(A_4 = 120 + \frac{1}{4}A_3 = 120 + \frac{1}{4}*159\)...
The terms are increasing in value.
Thus, A₁₂ > 159.


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If An+1=120 + (1/4)An for each positive integer n, and A1=150, which o  [#permalink]

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New post 27 Jun 2018, 02:24
1
MathRevolution wrote:
[GMAT math practice question]

If An+1=\(120 + (\frac{1}{4})\)An for each positive integer \(n\), and A1=150, which of these ranges of values includes A12?

A. 110-120
B. 120-130
C.130-140
D. 140-150
E. 150-160


We are given An+1=\(120 + (\frac{1}{4})\)An

A2 = \(120 + (\frac{1}{4})*150 = \frac{630}{4}\) (As A1=150)

A3 = \(120 + (\frac{1}{4}\))A2 = \(120 + (\frac{1}{4} * \frac{630}{4}) = 120 + 37.5 = 157.5\) (As A2=\(\frac{630}{4}\))

We can repeat this process until A12 and the value will only increase from this value.

Therefore, the range of the values that can be a possible value for A12 is Option E(150 - 160)
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If An+1=120 + (1/4)An for each positive integer n, and A1=150, which o  [#permalink]

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New post 29 Jun 2018, 00:17
=>

A1 = 150, A2 = \(120 + (\frac{1}{4})150 = 120 + 32.5 = 152.5.\) As An is increasing,
A12 must lie between \(150\) and \(160\).

Therefore, the answer is E.

Answer: E
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If An+1=120 + (1/4)An for each positive integer n, and A1=150, which o &nbs [#permalink] 29 Jun 2018, 00:17
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