# Sequences and series (1)

Algebra Level 5

Find the sum of the terms of the Geometric Progression, $$a+ar+ar^2 + ar^3 + \cdots$$, where $$a$$ is the value of $$x$$ for which the function $$7+2x \ln 25 -5^{x-1} - 5^{2-x}$$ has a greatest value and $$r$$ is equal to $$\displaystyle\lim_{x\rightarrow 0} \displaystyle\int_{0}^{x} \frac{t^2 dt}{x^2 \tan (π+x)}$$

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