Question

Which term of the progression 20,77/4,17/2,71/4,............is the first negative

Answer 1

Answer:

28th term

-1/4

Step-by-step explanation:

Which term of the progression 20,77/4,17/2,71/4,............is the first negative

17/2 is typed wrong its should be 37/2 = 74/4

then AP would be

80/4  , 77/4  , 74/4  , 71/4

20 , 77/4 , 37/2 , 71/4

with a = 80/4

d = -3/4

let say nth term is 1st -ve

nth term = a + (n-1)d

nth term = 80/4  + (n-1)(-3/4)

nth term = (1/4)( 80 -3n + 3)

nth term = (1/4)(83-3n)

nth term is -ve

so nth term < 0

(1/4)(83 -3n) < 0

83 - 3n <0

-3n < -83  

3n > 83  ( on cancelling -ve sign the < and > get interchanged)

n > 83/3

n > 27.67

n = 28

28th term = 20 + (28-1)(-3/4)

= 20 - 81/4

= (80-81/4)

= - 1/4