which term of the AP 20,19(1/4),18(1/2),17(3/4) is the first negative term find the term also
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Given AP is 20, 19.25, 18.5, 17.75 ……
Here first term a = 20
Common difference d = 19.25 - 20 = -0.75
Let the first negative term be n
Tn = a + (n-1)d
=> n = 20 + (n-1) *(-0.75) < 0
=> 20 - 0.75n + 0.75 < 0
=> -0.75n < - 20.75
=> n > 20.75/0.75
=> n > 27.6
Since n is a term , so it's a natural number , & immediate natural number next to 27 is 28
=> n = 28
So, 28 th term is the first negative number.
VERIFICATION:
T28 = 20 + 27*(-0.75)
= 20 - 20.25
= - 0.25
Here first term a = 20
Common difference d = 19.25 - 20 = -0.75
Let the first negative term be n
Tn = a + (n-1)d
=> n = 20 + (n-1) *(-0.75) < 0
=> 20 - 0.75n + 0.75 < 0
=> -0.75n < - 20.75
=> n > 20.75/0.75
=> n > 27.6
Since n is a term , so it's a natural number , & immediate natural number next to 27 is 28
=> n = 28
So, 28 th term is the first negative number.
VERIFICATION:
T28 = 20 + 27*(-0.75)
= 20 - 20.25
= - 0.25
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