$a, b, c, d, e$ are five numbers in which the first three are in AP and the last three are in HP. If the three numbers in the middle are in GP then the numbers in the odd places are in

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Solution

The correct option is B GP
Given
$2 b = a + c$ and $d = \frac{2 c e}{c + e}$
Also, $c^{2} = b d$
$\Rightarrow c^{2} = \frac{a + c}{2} \times \frac{2 c e}{c + e}$
$\Rightarrow c (c + e) = a e + c e$
$\Rightarrow c^{2} = a e$
$∴$ $a, c, e$ are in GP.

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a,b,c,d,e are five numbers in which the first three are in AP and the last three are in HP. If the three numbers in the middle are in GP then the numbers in the odd places are in

The correct option is B GPGiven2b=a+c and d=2cec+eAlso, c2=bd⇒c2=a+c2×2cec+e⇒c(c+e)=ae+ce⇒c2=ae∴ a,c,e are in GP.

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$2 b = a + c$ and $d = \frac{2 c e}{c + e}$
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