Question

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

Answer 1

Answer:

The first negative term of the given AP is 24th term.

Step-by-step explanation:

Given :  

a = 114, common difference,(d) = a3 – a2 = a2 – a1 =  109 - 114 = - 5

Let , nth term of this AP be the first negative term .  

Then , an < 0

a + (n – 1)d < 0

114 + (n – 1) (– 5) < 0

114 – 5n + 5 < 0

119 – 5n < 0

119 < 5n

5n > 119

n > 119/5

n > 23 ⅘  

Least integral value of n is 24  

Hence, first negative term of the given AP is 24th term.

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Answer 2

Answer

a = 114

d = -5

an = 0

an = a + (n-1)d

0 = 114 - 5 (n-1)

n = 114/5 + 1

n = 23.8

Thus, first negative term = 24