Question

For what value of n the ap 50 47 44.... is negative

Answer 1

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Here is your answer...✌️

GIVEN
AP : 50 , 47 , 44 ,...

=> a = 50

=> d = 47 - 50
=> d = -3

We have to find negative terms of AP

i.e., Tn < 0

a + (n-1)d < 0

50 + (n-1)(-3) < 0

50 - 3n + 3 < 0

53 - 3n < 0

- 3n < -53

3n > 53

n > 53/3 ( or 17.66 )

=> n = 18 is the first negative term of given AP

HENCE,

For n ≥ 18
The AP is negative

Answer 2

A=50
D=47-50= -3
let the last number or first negative number
An= -1
Using formula
An=A+(n-1)D
putting the values
-1=50+(n-1)-3
-1-50=(n-1)-3
-51=(n-1)-3
-51/-3=n-1
17=n-1
17+1=n
n=18
so first negative number is 18th term
verification,
An=50+(18-1)-3
An=50+(17)-3
An=50+(-51)
An= -1
Hence proved
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