Question 30
The sum of the first $n$ terms of an arithmetic progression with first term $m$ and difference $2$ is equal to the sum of the first $n$ terms of a geometric progression with first term $n$ and ratio $2$.
a) Prove that $m+n=2^{m}$;
b) Find $m$ and $n$, if the third term of the geometric progression is equal to the $23$-rd term of the arithmetic progression.
a) Prove that $m+n=2^{m}$;
b) Find $m$ and $n$, if the third term of the geometric progression is equal to the $23$-rd term of the arithmetic progression.