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When school closes, A school uses the phone tree to contact each student’s family, the principal’s secretary calls three families, then each family calls 3 other families and so on. How many families will be notified during the 7th round of calls?

Last updated date: 26th Feb 2024
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IVSAT 2024
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Hint: In the given question families are called by the principal’s secretary initially and then other families are called by the already called family and this is how the chain goes on. Now, we are being asked to find the number of families that would be present at the seventh step of this chain and how.

Complete step by step answer:
According to the question, initially the principal’s secretary has called 3 families.
That is, in the first round there are 3 families.
Now these three families are called other three families therefore the second-round number of families becomes ${{3}^{2}}=9$.
Now again these 9 families call the other families which is equal to ${{3}^{3}}=27$ and this is how the chain goes on. Now we can clearly see the pattern that the number of families is given by${{3}^{n}}$where n is the number of rounds.
Therefore, in the seventh round the number of families would be ${{3}^{7}}=2187$ .
Therefore, we can say that 2187 families were notified at the seventh round of the call.

Note: In such a type of question, we basically have to catch the concept and logic behind the question. All we need is to be aware of the concept of the power and exponent and do it accordingly and there are very chances of error in this question as we just need to evaluate the number raised to some power 7 which can be done directly also if there is no time constraint and the base number is small.