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If An+1=120 + (1/4)An for each positive integer n, and A1=15

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by Max@Math Revolution » Wed Jun 27, 2018 12:50 am

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[GMAT math practice question]

If An+1=120 + (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
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by GMATGuruNY » Wed Jun 27, 2018 2:08 am
Max@Math Revolution wrote:[GMAT math practice question]

If An+1=120 + (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
A₂ = 120 + (1/4)(A�) = 120 + (1/4)(150) = 120 + 37.5 = 157.5.
A₃ = 120 + (1/4)(A₂) = 120 + (1/4)(157.5) ≈ 120 + 39 = 159.
A₄ = 120 + (1/4)(A₃) = 120 + (1/4)(159)...
The results above indicate that the terms are increasing in value.
Thus, A�₂ > 159.

The correct answer is E.
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by Max@Math Revolution » Fri Jun 29, 2018 12:06 am
=>

A1 = 150, A2 = 120 + (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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