Find first negetive term in the following AP 18 , 16½ , 13 , ----------
Answers
Answer:
understand
Step-by-step explanation:
8th term is first negative term. The first negative term is -2.
Step-by-step explanation:
The given AP is
19, 16, 13,...
First term = 19
Common difference = 16 - 19 = -3
nth term of AP is
a_n=a+(n-1)da
n
=a+(n−1)d
where, a is first term and d is common difference.
Substitute a=19 and d=-3.
a_n=19+(n-1)(-3)a
n
=19+(n−1)(−3)
a_n=19-3n+3a
n
=19−3n+3
a_n=22-3na
n
=22−3n .... (1)
We need to find the first negative term.
a_n < 0a
n
<0
22-3n < 022−3n<0
22 < 3n22<3n
\dfrac{22}{3} < n
3
22
<n
7.3333.. < n7.3333..<n
n is greater than 7. It means 8th term is first negative term.
Substituted n=8 in equation (1) to find the 8th term.
a_n=22-3(8)=22-24=-2a
n
=22−3(8)=22−24=−2
Therefore, first negative term is -2.
Answer:
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