Question
Sun December 16, 2012 By:
 

hoe can we get the first negativ e term of an ap like 20, 19*1/4, 18*1/2, ......................... and the term

Expert Reply
Tue December 18, 2012

The given A.P is 20, 19 (1/4), 18 (1/2), 17 (3/4),......

Hence, a = 20

d = 19 (1/4) - 20 = -(3/4)

Let the nth term of the A.P be the first negative term. Then,

an < 0

=> a + (n - 1) d

=> 20 + (n - 1) (-3/4) < 0

=> 20 < (n - 1) (3/4)

=> (n - 1) (3/4) > 20

=> (n - 1) > 20/ (3/4)

=> (n - 1) > 20 x 4/3

=> (n - 1) > 80/3

=> n > 80/3 + 1

=> n > (80 + 3)/3

=> n > 83/ 3

=> n > 27 (2/3)

Least integral value of n = 28. Hence, 28nd term of the given A.P is the first negative term .

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