Question

Which terms of progression 19,18 1/5,17 2/5 is the first negative term

Answer 1

Answer:

11th

Maths

Sequences and Series

Arithmetic Progression

Which term of the AP, 19, 1...

MATHS

Which term of the AP, 19,18

5

1

,17

5

2

,... is the first negative term?

EASY

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ANSWER

We must find the common difference of the A.P:-

Common difference (d)=firstterm−secondterm

=18

5

1

−19

=

5

91

−

5

95

=

5

−4

Hence,

the common difference is

5

−4

or−0.8

Now to estimate which term of this A.P will be negative let us assume

the nth therm of A.P IS 0.

Formula for the nth term of an A.P is =a+(n−1)d

then,

0=19+(n−1)×−0.8

0=19−0.8n+0.8

0.8n=19.8

n=

0.8

19.8

n=24.75

if the 24.75th term is 0. Then surly 25th term of the

A.P will be negative.

Let us make sure, just in this case:

25thtermofanA.P=a+(n−1)d

=19+(25−1)×−0.8

=19+(24×−0.8)

=19+(−19.2)

=19−19.2

=−0.2

Thus, the 25th term of the progression is first negative term.

Hence,

option B is correct answer.