Question

Find the sum of the first 9 terms of the following sequence. Round to the nearest hundredth if necessary. 6, comma, 15, comma, start fraction, 75, divided by, 2, end fraction, comma, point, point, . 6,15, 2/75 ​ ,...

Answer 1

Explanation:

Find the sum of the first 9 terms of the following sequence. Round to the nearest hundredth if necessary.
6, 15,75/2,...

This is a geometric sequence with

first term equal to 6

and common ratio is 15/6=5/2

`6+15+(75)/(2) +...\\sum=6+6*(5)/(2) +6*((5)/(2) )^2+6*((5)/(2) )^3+...+6*((5)/(2) )^8\\=6*\frac{{((5)/(2))}^9-1}{(5)/(2)-1} \\\\=6*\frac{(1953125)/(512)-1} {(5)/(2) -1}\\\\\\=(1952613)/(128) \\\\=15254.7890625\\\\\approx{15254.79}`