which time is the first negative turn in the given a p 23, 21 into 1 by 2, 20,
Answers
Step-by-step explanation:
The 17th term is the first negative term in the given A.P, i.e. -1.
Step-by-step explanation:
The given AP is
23,21.5 ,20....
The first term is 23 and the common difference is -1.5.
a=23, d=-1.5a=23,d=−1.5
The nth term of an AP is
a_n=a+(n-1)da
n
=a+(n−1)d
a_n=23+(n-1)(-1.5)a
n
=23+(n−1)(−1.5)
nth term is negative.
a_n<0a
n
<0
23+(n-1)(-1.5)<023+(n−1)(−1.5)<0
23-1.5n+1.5<023−1.5n+1.5<0
24.5-1.5n<024.5−1.5n<0
24.5<1.5n24.5<1.5n
\frac{24.5}{1.5}
16.333
It means for negative terms the value of n must be greater than 16.33. The first negative term is 17 th term.
a_{17}=23+(17-1)(-1.5)a
17
=23+(17−1)(−1.5)
a_{17}=23+(16)(-1.5)=-1a
17
=23+(16)(−1.5)=−1
Therefore the 17th term is the first negative term in the given A.P, i.e. -1.
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