SSAT Math Question 353: Answer and Explanation
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Question: 353
12. If Jeeves deposits $100 in a bank account that will double his money every 20 years, after how many years will his bank account be worth $1,600?
- A. 5
- B. 10
- C. 50
- D. 80
Correct Answer: D
Explanation:
The answer is D
The value of the nth term, Sn, of a geometric sequence is given by the equation Sn = S1(rn - 1), where S1 is the first term and r is the common ratio between terms. Here, the first term is $100, the final term is $1,600, and the common ratio is 2. Use these numbers in the equation: $1,600 = $100(2n - 1). Divide both sides by $100: 16 = 2n - 1. As 16 = 24, n = 5. This means that $1,600 is the fifth term and, therefore, there were four increases from $100. The question indicates that each increase takes place over 20 years, so multiply 4 by 20: 80.
You can quickly write out the amounts he has, in 20-year peri