Which term of the AP : …
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Yogita Ingle 6 years, 10 months ago
Given AP is:
121, 117, 113, ................
First term a = 121
Common difference d = 117-121 = -4
Let nth term is the first negative term in AP
Now nth tern in AP = a + (n-1)*d
= 121 + (n - 1)*(-4)
= 121 - 4n + 4
= 125 - 4n
Now, we have to find the suitable value of n so that the value of (125 - 4n) is negative.
⇒ 125 - 4n < 0
⇒ 125 < 4n
⇒ 4n > 125
⇒ n > 125/4
=> n > 31.25
Since the term can not be in decimal form (term is always taken a positive integer)
So, n = 32
Now, by taking value of n = 32, we get
nth term = 125 - 4× 32 = 125 - 128 = -3
This is the first negative term in the series.
So, n = 32
Hence, the 32nd term is the first negative term in AP.
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