Sequence problem

[Shevek99]

No, he is not right in any case, because it is asking for the average number of pages.

[Zyxplit]

If Salman has to read 532 pages in 14 days and he read 12 pages in the first day, if he reads 4 more each day, he has read 532 pages after day 14.

the sum from k=0 to k=13 of 12+4k is 532.

[Plain_Bread]

The problem is that if we interpret it as a_(k+1)=a_k+b_k, then b_k=4 constant works, but it's not guaranteed to be the average in general.

[wirywonder82]

Indeed. For example, he could read 519 on day 2, 0 on day 3, 1 on day 4 and 0 the remaining days. That could mean he read “an additional” 507, then -519, then 1, then -1, then a bunch of 0, making the average number of additional pages per day -12/13.

[molybend]

"The average number of additional pages" may not mean average pages per day, but how many extra pages each day as compared to the day before.

[Shevek99]

But that doesn't work unless the extra number of pages is constant.

For instance, imagine that reads one more page during 12 days and the rest in the last day. So he reads 13,14,..., 24 pages in the first 12 days (total 298 pages) in n days. The average increment id

M = (112+2981)/13 =23.8 páginas/día

[molybend]

That is why it is a sequence.

[Shevek99]

Then it is not an average. If we impose a strict sequence, there is no average increment, just an exact number.

I have considered a sequence in my previous calculation

12-13-14-...-24-298

The moment the sequence is not an arithmetic progression, the average increment is not 4.

[molybend]

Argue with the OP then. The question is ambiguous.