Question

Найдите а[15] + а[30], если известно, что а[14] + а[16] = -8 и a[29] + а[31] = 44

Answer 1

$\left \{ {{a _{14} +a _{16}=-8 } \atop {a _{29}+a _{31}=44 }} \right. \\\\ \left \{ {{a _{1}+13d+a _{1} +15d=-8 } \atop {a _{1}+28d+a _{1} +30d=44 }} \right.\\\\ \left \{ {{2a _{1}+28d=-8 } \atop {2a _{1}+58d=44 }} \right.\\\\ +\left \{ {{a _{1}+14d=-4 } \atop {a _{1}+29d=22 }} \right.$
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2a₁ + 43d = 18
a₁₅ + a₃₀ = a₁ + 14d + a₁ + 29d = 2a₁ + 43d = 18