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An amphitheatro has 17 seats in the first row, 20 in the second, 23 in the third, and so on, for 27 rows. How many seats are in the amphitheatre? The amphitheatre has seats

User Vivek Viswanathan
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1 Answer

11 votes
11 votes

Answer:

The amphitheatre has;


1512\text{ seats}

Step-by-step explanation:

The number of seats in each row represent an arithemetic sequence;


17,20,23,\ldots

since there are 27 rows the number of seats in the last row will be;


\begin{gathered} a_(27)=a+(n-1)d \\ a=17\text{ first term} \\ d=20-17=3\text{ common difference} \\ a_(27)=17+(27-1)3 \\ a_(27)=95 \end{gathered}

The sum of all the seats in the amphitheatre will be;


\begin{gathered} S_(27)=(n)/(2)(a+a_(27)) \\ S_(27)=(27)/(2)(17+95) \\ S_(27)=(27)/(2)(112) \\ S_(27)=1512 \end{gathered}

Therefore, The amphitheatre has;


1512\text{ seats}
User Wouch
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