if i did one push up on Jan 1st 2014 and I did two push ups the next day Jan 2 2014 than 3 times on Jan 3rd 2014 what would I be at by the end of the year? How many pushups would I have done throughout the whole year?
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5http://en.wikipedia.org/wiki/Triangular_number – Jan 06 '14 at 07:17
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266,795. ${}{}{}{}$ – copper.hat Jan 06 '14 at 07:21
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@Devon, 3 times of first day or 3 times of second day? – Vikram Jan 06 '14 at 07:26
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What have you tried so far? Where do you have difficulties? What you are trying to evaluate is $1+2+3+...+365$. Have you ever seen this sum? – Umberto Jan 06 '14 at 08:07
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Ask your twin brother to do 365 pushups on Jan 1st, 364 pushups on Jan 2nd, ..., 2 pushups on Dec 3oth, and 1 pushup on Dec 31st.
- How many pushups do you and your twin brother do in total each day?
- How many pushups do you and your twin brother do in total in the whole year?
- How many pushups does each of you do in the whole year?
TonyK
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Go by Arithmetic Series formula.
Sum of first n terms of an A.P. is Sn = (n/2)[2a +(n -1)d]
1+2+3+...+365 = (365/2)*(2*1+(365-1)*1) = 66795
Surajit Biswas
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You do $1$ push-up on the first day, $2$ on the second, and generally $n$ push-ups on day $d_n$. So, on the day $d_{365}$, you will do 365 push-ups.
The total number of push-ups is $T=1+2+3+...+365$
Note, you can also write this as $T=365+364+363+...+1$.
Add these two, thus getting:$2T=366+366+...365\text{ times}$
So, ${T}={{366×365}\over{2}}={66795}$
DynamoBlaze
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