# Questions tagged [arithmetic-progressions]

Questions related to arithmetic progressions, which are sequences of numbers such that the difference between consecutive terms is constant

559 questions
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### Prouhet-Thue-Morse sequence and Arithmetic Progressions

This question is a fragment from a question posted by @Mathphile for which the link will be provided below. Let $(x_i)$ be an arithmetic progression of length $M$. Let $(t_i)$ be the $i$th element in ...
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### Expression for the sum of another bounded series with arithmetic and geometric components

The expression I have is the following: $S = \sum_{i=1}^T (1-q)^{i-1}i$ My expression after I play around with it is: $S= \frac{1-(1-q)^TT}{q}+\frac{1-q}{q} \left(\frac{1-(1-q)^{T-1}}{q} \right)$...
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### Arithmetic sequence questions

Consider the arithmetic sequence 34252, 34235, 34218,... Find that last positive term in the sequence. Since the sequence is decreasing so the formula is $a_n=-17n+34269$ for finding the nth term ...
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### Let $a^2,b^2,c^2$ be natural numbers in an arithmetic progression with difference $k$.show that $24\mid k$

I need to solve the following question: Let $a^2,b^2,c^2$ be natural numbers in an arithmetic progression, with difference $k$. Show that $24\mid k$. I'm just learning the basics of number theory ...
1answer
18 views