First slide

Geometric progression

Question

Three numbers a,b,c are between 2 and 18 such that their sum is 25 and 2,a,b are A.P and b,c,18 are in G.P then abc is

Moderate

A

360
B

420
C

480
D

540

Solution

$g i v e n t h a t a + b + c = 25 \to (1) \sin c e 2, a, b a r e i n A . P \Rightarrow$
$\begin{array}{l} 2 + b = 2 a - - - - (2) \\ b, c, 18 are in G \cdot P \Rightarrow 18 b = c^{2} - \dots - (3) \\ (1) and (2), eliminate a \Rightarrow 3 b + 2 c = 48 - - - - (4) \\ (3) and (4) \Rightarrow c^{2} + 12 c = 288 \to c = 12, - 24 \\ \to c \in (2, 18) \Rightarrow c = 12, b = 8, a = 5 \to abc = 480 \end{array}$

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