Question

Which term of the A.P. : 120, 116, 112, ….. is its first negative term.

Answer 1

SOLUTION

TO DETERMINE

Which term of the A.P. : 120, 116, 112, ….. is its first negative term.

EVALUATION

Here the given Arithmetic progression is

120, 116, 112, …..

First term = a = 120

Common Difference = d = 116 - 120 = - 4

Let n th term be the first negative term

Now n th term of the Arithmetic progression

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

$\sf{ = 120 - 4 (n - 1) }$

$\sf{ = 120 - 4 n + 4 }$

$\sf{ = 124 - 4 n }$

So by the given condition

$\sf{124 - 4n < 0}$

$\sf{ \implies \: 4n > 124}$

$\sf{ \implies \: n > 31}$

So 32 th term is the first negative term

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