Question

which term of the ap 20,17,,14........is first negative term​

Answer 1

Step-by-step explanation:

Given,

AP : 20, 17, 14,........

a = 20

d = -3

Let, a(n) be 0.

So, 20 + (n-1)×(-3) =0

-3n +3 = -20

n = 23/3 = 7.666...

There is no term that is 0.

Therefore, the 8th term of the AP is the first negative term.

Verification: a8 = a + 7d

= 20 + 7×(-3)

= 20 - 21

= -1.

Answer 2

Step-by-step explanation:

In the given A.P.

First term = 20

Common difference = 2nd term - First term

= 17 - 20 = - 3

Let the nth term of the given A.P. be first negative term.

Since nth term is the first negative term,

Therefore, nth term is less than zero.

So,

nth term of the A.P < 0

=> a + (n - 1)d < 0

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

=> 20 - 3n + 3 < 0

=> 23 - 3n < 0

=> 23 < 3n

=> n > 23/3

=> n > 7.66

Since n is greater than 7.

Therefore,

8th term of the given A.P. is the first negative term.

8th term is : 20 + (8 - 1) *(- 3)

= 20*(- 21)

= - 21

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