Question

61. Найдите разность арифметической прогрессии, если а¹ + a⁵ = 24, а²•а³, = 60. А) 4 B) 14 C) 5 D) 3 E) 7

Answer 1

$a _{n} = a_{1} + d(n - 1)$

$a _{5} = a _{1} + 4d$

$a_{1} + a_{1} + 4d = 24$

$2a_{1} + 4d = 24 \\ 2a_{1} = 24 - 4d \\ a_{1} = \frac{2(12 - 2d)}{2} \\ a_{1} = 12 - 2d$

$a_{2} = a_{1} + d \\ a_{3} = a_{1} + 2d$

$(a_{1} + d)(a_{1} + 2d) = 60 \\ (12 - 2d + d)(12 - 2d + 2d) = 60 \\ (12 - d) \times 12 = 60 \\ 12 - d = \frac{60}{12} \\ 12 - d = 5 \\ d = 5 - 12 \\ - d = - 7 \\ d = 7$

Разность 7