The resulting chemical formulae are Mg3N2, Li3N, Na2S and Al2O3. In each compound, the combining valencies of the metal and non-metal elements are criss-crossed to establish an electrically neutral ionic substance.
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Calculating values gives 1, 2, 3, 5, 8, 13, 21, 34. Subtracting consecutive terms reveals Wn – Wn-1 = Wn-2, which means Wn = Wn-1 + Wn-2. This is the Virahanka-Fibonacci sequence.
Computing terms yields 1, 2, 4, 8, 16, 32, 64, 128. Since Pn – Pn-1 = Pn-1, the simpler recursive rule is Pn = 2Pn-1 for n >= 3. The explicit formula is Pn = 2ⁿ⁻¹ for n >= 2 ...
Using a(1 + r + r²) = 26 and a²(1 + r² + r⁴) = 364, dividing squares gives (1 + r + r²) / (1 – r + r²) = 13/7, leading to r = 3 or 1/3. The ...
Writing x = ar³, y = ar⁹ and z = ar¹⁵, we compute y² = (ar⁹)² = a²r¹⁸. Also x x z = (ar³) x (ar¹⁵) = a²r¹⁸. Since y² = x x z, x, y, z form a GP.