Find the sum of the first 8 terms of the following sequence. Round to the nearest hundredth if necessary. 100,123, 151.29, __ Sum of a finite geometric series: S_(n)=(a_(1)-a_(1)r^n)/(1-r) Answer Attempt 2 out of 2 square

To find the sum of the first 8 terms of the given sequence, we need to identify the common ratio (r) and the first term (a1).<br /><br />Given sequence: 100, 123, 151.29,...<br /><br />Step 1: Find the common ratio (r).<br />To find the common ratio, we can divide any term by its previous term.<br />r = 123 / 100 = 1.23<br /><br />Step 2: Find the first term (a1).<br />The first term (a1) is the first number in the sequence.<br />a1 = 100<br /><br />Step 3: Use the formula for the sum of a finite geometric series.<br />The formula for the sum of a finite geometric series is:<br />$S_{n}=\frac {a_{1}-a_{1}r^{n}}{1-r}$<br /><br />Step 4: Substitute the values into the formula.<br />$S_{8}=\frac {100-100(1.23)^{8}}{1-1.23}$<br /><br />Step 5: Calculate the sum.<br />$S_{8}=\frac {100-100(1.23)^{8}}{1-1.23} \approx 1000.00$<br /><br />Therefore, the sum of the first 8 terms of the given sequence is approximately 1000.00.