Question

# Find the missing number.$120,80,40,45,?,5$

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Solution

## Find the missing number.The given series is, $120,80,40,45,?,5$It is observed that the given series is the combination of two different series $120,80,40\mathrm{and}45,?,5$.The first series $120,80,40$ are in AP where the common difference is $-40$.As we know, the difference between two consecutive terms of arithmetic progression always remains the same.Let the unknown number is $x$$\therefore x-45=5-x\phantom{\rule{0ex}{0ex}}⇒x+x=5+45\phantom{\rule{0ex}{0ex}}⇒2x=50\phantom{\rule{0ex}{0ex}}⇒x=\frac{50}{2}\phantom{\rule{0ex}{0ex}}⇒x=25$Hence, the missing number is $25$.

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