Question

A1=5,A4=19/2 find A2 and A3 it is in progressions

Answer 1

$a = 5 \: \: \: \: and \: \: \: \: a_{4} = \frac{19}{2} \\ \\ \: \: \: \: \: \: \: \: \: a_{n} = a + (n - 1)d \\ = > \frac{19}{2} = 5 + (4 - 1)d \\ = > \: 3d = \frac{19}{2} - 5 \\ = > \: 3d = \frac{19 - 10}{2} \\ = > \: \: \: d = \frac{9}{3 \times 2} \\ = > \: \: \: d = \frac{3}{2}$

$Now,\: \\ a_{n} = a + (n - 1)d \\ \\ a_{2} = 5 + (2 - 1) \times \frac{3}{2} = 5 + \frac{3}{2} = \frac{10 + 3}{2} = \frac{13}{2} \\ \\ a_{3} = 5 + (3 - 1) \times \frac{3}{2} = 5 + (2) \times \frac{3}{2} = 5 + 3 = 8$