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