Which term of the AP 121, 117, 113, ... is its first negative term?

Here, First term = a = 121

Common difference = d = 117 - 121 = - 4

Let nth term of the AP be its first negative term.

an <0

Since, nth term of an AP is given by:

an = a + (n - 1)d

a + (n - 1)d < 0

121 + (n - 1) × (-4) < 0

- 4n + 125 < 0

- 4n < - 125

4n > 125

n > 31.25

Since n is an integer, therefore n must be 32.

32nd term will be the first negative term of the AP.

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