Question

Which term of the AP. 20, 17, 14, .........; is the
first negative term ?

• A. 8th
• B. 6th
• C. 9th
• D. 7th

Answer 1

Answer: (A)

8th

The given sequence is 20, 17, 14, ..............
The nth term of this sequence is given by $t_n=a+(n-1)d$.
To find the first negative term, $t_n$ should be less than 0.
We have 'a' = 20, 'd' = -3
$a+(n-1)d<0$
$⟹20+(n-1)(-3)<0⟹20+3-3n<0⟹23-3n<0⟹3n>23orn>\frac{23}{3}$.
The next natural number greater than 7.6 is 8.
Hence, the 8th term is the first negative number.