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jmc

algebra intermediate

Problem

Jasmine had 3 paperclips on Monday, then she had 6 on Tuesday, and her number of paperclips proceeded to double on each subsequent day. On what day of the week did she first have more than 100 paperclips?
Solution
This is a geometric sequence with first term 3 and common ratio 2. Thus, any term in this sequence can be represented as for some non-negative integer , where represents the term number (for example, when , , which is the term of the sequence). We need to find the smallest such that . Using trial and error, we find that , which means that the day is the the one on which Jasmine has more than 100 paperclips, or .
Final answer
\text{Sunday}