Question

Which term of the AP 20, 17, 14, .... is the first negative term.

Answer 1

Answer:

=> 20, 17, 14,......... is an A.P

=> let last term of an A.P is 0

=> means, an =0

=> now, a = 20

=> d = 17 - 20 = -3

=> an =0

=> n =?

=> an = a +( n -1)d

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

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

=> 20/3 = n - 1

=> 20 / 3 +1 =n

=> 20 +3/ 3 = n

=> 23 / 3 = n

=> n = 7.6666

=> therefore,

=> an = 0, n = 7.66

therefore

=> the first negative term, n = 8

Hope it helps you..

Answer 2

Answer:

let a & d be the first term & the common difference respectively

a = 20

d = 17 - 20 = -3

now we know that the very next term after 0 is always negative

i.e $t_{n} = 0$

$t_{n} = a +(n - 1)d\\\\0 = 20 + (n-1)(-3)\\\\0 = 20 - 3n + 3\\\\-23 = -3n\\\\n = \frac{23}{3}\\\\n = 7\frac{2}{3}$

since n is coming in fraction it means that this AP will not have 0 as it's term

so we will look at the whole value of n

i.e  7

so if we consider that 0 comes in this AP and it will be the value of 7th term

thus the 8th term of this AP will be the first negative term

I hope it helps .......