1}if x+4,3x-2,4x-2 .............are in a.p (a)find the value of x? (b)write the sequence? (c)find the nth term of the sequence? 2}Two person are standing at opposite direction of flag post at of height 75m at an equal distance from the base of the flag post and looking the tip of the flag post at an angle of 45 . find the distance between two person?

Let the sequence be x + 4, 3x – 2, 4x – 2..............

d = a₂ – a₁

= (3x – 2) – (x + 4)

= 3x – 2 – x – 4 = 2x – 6

d = a₃ – a₂

= (4x – 2) - (3x – 2)

= 4x – 2 – 3x + 2 = x

2x – 6 = x

2x – x = 6

x = 6

The sequence is

6 + 4, 3 * 6 – 2, 4 * 6 – 2, …..

10, 16, 22

n^th term = a + (n - 1)d

a= 10, d = 6

= 10 + ( n – 1 ) 6

= 10 + 6n – 6

= 6n + 4