Question

10/10
how many guests can be seated at 10 tables if the first table seats 9 and each subsequent table seats 6 more guests?
63
69
66
60

Explanation:

Step1: Identify sequence parameters

First term $a_1 = 9$, common difference $d = 6$, number of terms $n = 10$.

Step2: Find nth term of sequence

Formula for nth term: $a_n = a_1 + (n-1)d$
$a_{10} = 9 + (10-1)\times6 = 9 + 54 = 63$

Step3: Calculate total number of guests

Sum of arithmetic sequence: $S_n = \frac{n}{2}(a_1 + a_n)$
$S_{10} = \frac{10}{2}(9 + 63) = 5\times72 = 360$

Wait, correction: The options provided do not match the total sum, which means the question was misinterpreted. Re-reading: the question may ask for the number of guests at the 10th table, not total.

Step1: Identify sequence parameters

First term $a_1 = 9$, common difference $d = 6$, $n = 10$.

Step2: Compute 10th table capacity

$a_n = a_1 + (n-1)d$
$a_{10} = 9 + (10-1)\times6 = 9 + 54 = 63$

Answer:

63