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Q.

If the arithmetic mean and geometric mean of the pth and qth terms of the sequence −16,8,−4,2,..... satisfy the equation 4x2−9x+5=0 , then  p+q is equal to _______.

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answer is 10.

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Detailed Solution

tp=−16−12p−1=−1p25−ptq=−16−12q−1=−1q25−qThe arithmetic mean of the above two terms is 54 and geometric mean is 1−1p+q210−p−q=1⇒p+q=10
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