Question

which term of the ap 20 17 14.….…….…is the first negative term
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Answer 1

Hey Ma8 ,

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Common difference = 17-20 = 3

An < 0

20 + (n -1)3< 0

20 + 3n -3 < 0

17 +3n< 0

3n <.-17

n < -17 / 3

hence, -17/ 3 term of given AP is the 1st negative term

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Answer 2

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

a = 20 and a2 = 17

So , d( common difference) = a2 - a => 17 - 20= -3

Now let us assume that 0 is a term of this AP ,

So , by the formula :- A(n) = a + (n-1)d

We have ,

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

0 = 20 -3n + 3

0 = 23 - 3n

3n = 23

n = 23/3

n = 7.3

But n can't be in decimal

Hence here we know that the 7th term is the last positive term

Hence the first negative term is the 8th term

i.e ,

A(8) = 20 + (8-1)x(-3)

A(8) = 20 + 7x(-3) => 20 -21 = -1

Hope it helped you...