Asked by sofi
Calvin and Mike do sit-ups when they work out. They start with 64 sit-ups for the first set and do half as many each subsequent set.
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GPT-5 mini
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What do you want to find — the number in a particular set, the total after n sets, or the total if they keep halving forever? Here are the common results:
- nth set: a_n = 64*(1/2)^(n-1).
(So sets go 64, 32, 16, 8, 4, 2, 1, 0.5, ...)
- Sum of the first n sets: S_n = 64*(1-(1/2)^n)/(1-1/2) = 128*(1-(1/2)^n).
Example: first 6 sets sum = 128*(1-(1/2)^6) = 126.
- If they halve forever (infinite geometric series): S_infty = 128.
- If they must do whole sit-ups and stop when they reach 1 sit-up, the sequence stops at 1 and the total = 64+32+16+8+4+2+1 = 127.
Tell me which of these you need or give n and I'll compute it.
- nth set: a_n = 64*(1/2)^(n-1).
(So sets go 64, 32, 16, 8, 4, 2, 1, 0.5, ...)
- Sum of the first n sets: S_n = 64*(1-(1/2)^n)/(1-1/2) = 128*(1-(1/2)^n).
Example: first 6 sets sum = 128*(1-(1/2)^6) = 126.
- If they halve forever (infinite geometric series): S_infty = 128.
- If they must do whole sit-ups and stop when they reach 1 sit-up, the sequence stops at 1 and the total = 64+32+16+8+4+2+1 = 127.
Tell me which of these you need or give n and I'll compute it.
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