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MMO 007 Moscow MO 1935 system of arithmetic + geometric progression

Source:

July 17, 2019

Arithmetic Progressionalgebrasystem of equationsgeometric progression

Problem Statement

Find four consecutive terms

a, b, c, d

of an arithmetic progression and four consecutive terms

a_1, b_1, c_1, d_1

of a geometric progression such that

\begin{cases}a + a_1 = 27 \\\ b + b_1 = 27 \\ c + c_1 = 39 \\ d + d_1 = 87\end{cases}