Question

which term of the sequence 114,109,104....is the first negative term?

Answer 1

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Answer 2

Answer:

24th term is the first negative term.

Step-by-step explanation:

Given : Sequence 114,109,104....

To find : Which term of the sequence is the first negative term?

Solution :

Sequence 114,109,104.... is an Arithmetic progression.

Where, a=114 is the first term

d=109-114=-5 is the common difference

We know, $a_n<0$

So, n th term of the A.P is $a_n=a+(n-1)d$

i.e. $a+(n-1)d<0$

$114+(n-1)(-5)<0$

$114-5n+5<0$

$119-5n<0$

$5n>119$

$n>\frac{119}{5}$

$n>23.8$

i.e. $n>24$

Therefore, 24th term is the first negative term.