Problematic Progressions

Algebra Level 3

Two A.P's have the same number of terms. The ratio of the last term of the first progression to the first term of the second progressions equals the ratio of the last term of the second progression to the first term of the first progression both of which are numerically equal to \(4\). The ratio of the sum of the first \(k\) terms of the first to the second progression is equal to \(2\). Let \(\alpha\) be the ratio of the common difference of the first and the second progressions. Let \(\lambda\) be the ratio between their \(m\)th terms. Compute \(\alpha + 2\lambda\)

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