Find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence.
-As Sunee improves her algebra skills, she takes 0.9 times as long to complete each homework assignment as she took to complete the preceeding assignment. If it took her 60 minutes to complete her first assignment, find how long it took her to complete the fifth assignment. Find the total time she took to complete her first five homework assignments. (Round to the nearest minute.)
A) 39 min; 246 min
B) 35 min; 246 min
C) 39 min; 206 min
D) 35 min; 206 min

Question

Quizplus · Accepted Answer

The sum of the first n terms of a geometric sequence is given by the formula:$$S_n = a_1(1 - r^n) / (1 - r)$$where a_1 is the first term, r is the common ratio, and n is the number of terms.In this case, a_1 = 60 and r = 0.9. We want to find the sum of the first 5 terms, so n = 5.Plugging these values into the formula, we get:$$S_5 = 60(1 - 0.9^5) / (1 - 0.9)$$$$S_5 = 60(1 - 0.59049) / (0.1)$$$$S_5 = 60(0.40951) / (0.1)$$$$S_5 = 245.706$$Rounding to the nearest minute, we get 246 minutes.The fifth term of the sequence is given by the formula:$$a_n = a_1 * r^(n-1)$$Plugging in the values we know, we get:$$a_5 = 60 * 0.9^(5-1)$$$$a_5 = 60 * 0.9^4$$$$a_5 = 60 * 0.6561$$$$a_5 = 39.366$$Rounding to the nearest minute, we get 39 minutes.

Find the Indicated Sum