Question

please solve this guys urgent

Answer 1

given 5th term is zero
a+4d=0
a=-4d
33rd term is 4 times the 12th term 
a+32d=4(a+11d)
3a+12d=0
a+4d=0
it is valied condition 
hence it is proved

Answer 2

Note: We know that nth term of an AP = a + (n - 1) * d.

Now,

Given that 5th term of an AP is zero.

= > a + (5 - 1) * d = 0

= > a + 4d = 0.

= > a = -4d  --------- (1)


33rd term:

= > a + (33 - 1) * d

= > a + 32d

= > -4d + 32d

= > 28d         ----------------------- (2)


12th term:

= > a + (12 - 1) * d

= > a + 11d

= > -4d + 11d

= > 7d             ------------------------ (3)



From Equation (3) & (2), we can say that

33rd term = 4 * (12th term)



Hope this helps!