Question

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If the 4th ,10th and 16th terms of a GP are x, y and z respectively, then x,y,z are in GP
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Answer 1

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Answer 2

Answer:

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Let, α be the first term and r be the common ratio of the given GP.

$Then, T_{4} = x, T_{10} = y, T _{16} = z.$

$= > a {r}^{3} = x ,\: \: {ar}^{9} = 10 \: \: and \: \: {ar}^{15} = z$

$= {y}^{2} = ( {ar}^{9} )^{2} = {a}^{2} {r}^{18} \: and \: \: xz = ( {ar}^{3} )( {ar}^{15} ) = {a}^{2} {r}^{18}$

• Consequently, we've y² = xz
• Hence x, y, z are in GP .