Question

3. Знайдіть порядковий номер члена прогресії, якщо: 1) a, = 3, d = −5, a, =-37;
2) a, = −7, d = 2, an = 81. а, арифметичної​

Answer 1

$\displaystyle\bf\\1)\\\\a_{1} =3 \ \ \ ; \ \ \ d=-5 \ \ \ ; \ \ \ a_{n} =-37 \ \ \ ; \ \ \ n=?\\\\a_{n} =a_{1} +d\cdot(n-1)\\\\-37=3-5\cdot(n-1)\\\\-37=3-5n+5\\\\-37=-5n+8\\\\5n=8+37\\\\5n=45\\\\\boxed{n=9}\\\\\\2)\\\\a_{1} =-7 \ \ \ ; \ \ \ d=2 \ \ \ ; \ \ \ a_{n} =81 \ \ \ ; \ \ \ n=?\\\\a_{n} =a_{1} +d\cdot(n-1)\\\\81=-7+2\cdot(n-1)\\\\81=-7+2n-2\\\\81=2n-9\\\\2n=81+9\\\\2n=90\\\\\boxed{n=45}$