Question

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

Answer 1

The first negative term of the given sequence = 24

Step-by-step explanation:

The given sequence are:

114, 109, 104, ............

Here, first term (a) = 114, common difference (d) = 109 - 114 = - 5

The given sequence are in AP.

To find, the first negative term of the given sequence=

Let the first negative term = $a_{n}$

We know that,

The nth term of an A.P.

$a_{n}$ = a + (n -1)d

∴ 114 + (n -1)(-5) < 0

⇒ 114 - 5n + 5 < 0

⇒ 119 - 5n < 0

⇒ 5n > 119

⇒ n > $\dfrac{119}{5}$

⇒ n > 23.8

⇒ n = 24 (Since, the number of terms never be decimal)

Thus, the first negative term of the given sequence = 24

Answer 2

24 th term of sequence will be first negative term i.e. -1

•sequence is 114, 109, 104.....,4... with a=114 and d=-5

• as, An= a + (n-1)d

• 4=114+(n-1)(-5)

• -110= (n-1)(-5)

• n-1=22

• n=23

• next term to 4 is first negative term i.e. -1

• 24th term is first negative term