#844 · Algebra · Sequences & series

Relation of terms from sum ratios

If the sum of $m$ terms of an arithmetic progression is to the sum of $n$ terms as $m^{2}$ is to $n^{2}$ , show that the $m^{th}$ term is to the $n^{th}$ term as $2 m - 1$ is to $2 n - 1$ .

~6 minProof · checked by AIsum of arithmetic progressionterm ratio

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. IV. Arithmetical Progression, Examples IV.b, No. 18

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