Q. 14.3( 228 Votes )

# Which term of the AP: 121, 117, 113, . . ., isits first negative term?[Hint: Find n for ]

Here,
first term, a = 121
common difference, d = a2 - a1 = 117 - 121 = -4
Let the first negative term be 'an'.
Also, we know that, nth term of an AP is given by
an = a + (n - 1)d
We have to find least value of n, such that
an < 0
⇒ a + (n - 1)d < 0
⇒ 121 + (n - 1)(-4) < 0
⇒ 121 - 4(n - 1) < 0
⇒ 4(n - 1) > 121
⇒ 4n - 4 > 121
⇒ 4n > 125
⇒ n > 31.25
Therefore, n is 32 [least positive integer greater than 31.25 is 32]
Hence, the 32nd term of AP is first negative term.
Also,
a32 = a + 31d
= 121 + 31(-4)
= 121 - 124 = -3

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