Title MSTE 2 Solutions.pdf ✅

Since every day, the number of chickens decrease at a constant 25 chickens per day, then the amount of food per day is in an arithmetic sequence. S = n 2 [2a1 + (n − 1)d] 371250 = n 2 [2(4950) + (−25)(n − 1)] n = 100, 297 At n = 297, a297 = 4950 + (297 − 1)(−25) = −2450 < 0 It is an extraneous root. At n = 100, a100 = 4950 + (100 − 1)(−25) = 2475 > 0 Therefore, n = 100 days. ▣ 4. There are 20 geometric means between 488 and 36. Find the common ratio. [SOLUTION] From the given, a1 = 488, a22 = 36 From the formula for the general term, an = a1r n−1 36 = 488r 22−1 r = 0.88326 ▣ 5. The sum of three numbers in arithmetic progression is 45. If the first number is decreased by 4, the second number is decreased by 3, and the third number is increased by 14, the new numbers will be in geometric progression. Find the fifth term of the geometric progression. [SOLUTION] Let the three numbers be in the form: a − d, a, a + d. Express the sum (a − d) + a + (a + d) = 45 3a = 45 → a = 15 The three numbers become: 15 − d, 15, 15 + d Using the conditions for geometric progression, the numbers are (15 − d) − 4 = 11 − d 15 − 3 = 12