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Can someone help me what is the best formula for the following: I have $25$ as a starting number and as I increment I would add $25$ to my initial no. then sum up my 1st and 2nd no. Resulting to $50$ then increment again by $25$ and summing up the results of the 1st, 2nd and 3rd no. and so on..

\begin{array}{c c c} 1 & 25 & 25\\ 2 & 50 & 75\\ 3 & 75 & 150\\ 4 & 100 & 250 \end{array}

N. F. Taussig
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Jon Luna
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    Welcome to Maths SE. 2 things: I have reformatted your post but the input interpretation may be wrong so in future use this to learn how to format via $LaTeX$ and secondly, if someone gives an answer that is useful to you don't forget to tick it. All the best. – BLAZE Oct 13 '15 at 09:03

1 Answers1

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Let's denote the $i$-th number as $n_i$. We have $$ n_i = 25 \cdot 1 + 25 \cdot 2 + 25 \cdot 3 + \cdots + 25 \cdot i $$ (adding up the multiples of $25$). We know - from Gauß or at least attributed to him - that $$ \sum_{k=1}^i k = 1 + 2 + \cdots + i = \frac 12 i(i+1) $$ Hence $$ n_i = 25 \cdot (1+2+\cdots + i) = \frac{25}2 i(i+1) $$

martini
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