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 ...
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Given a + 10d = 38 and a + 15d = 73, subtracting gives 5d = 35, so d = 7 and a = -32. Using tn = a + (n – 1)d, the 31st term is -32 + 30 ...