Question

знайдіть 20-ий член арифметичної прогресії та суму пʼятнадцяти перших членів, якщо а6=8, а8=20

Answer 1

$\displaystyle\bf\\a_{6} =8\\\\a_{8} =20\\\\a_{20} =? \ \ ; \ \ S_{15} =?\\\\\\-\left \{ {{a_{1} +7d=20} \atop {a_{1}+5d=8 }} \right. \\---------\\a_{1} +7d-a_{1} -5d=20-8\\\\2d=12\\\\d=6\\\\a_{1} =8-5d=8-5\cdot 6=8-30=-22\\\\\\a_{20} =a_{1} +19d=-22+19\cdot 6=-22+114=92\\\\\\\boxed{a_{20}=92}\\\\\\S_{15} =\frac{2a_{1}+14d }{2} \cdot 15=(a_{1} +7d)\cdot15=a_{8} \cdot 15=20\cdot 15=300\\\\\\\boxed{S_{15} =300}$