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प्रश्न
Which term of the A.P. : 65, 61, 57, 53, .............. is the first negative term?
उत्तर
It is given that
AP : 65, 61, 57, 53
First term (a) = 65 and common difference (d) = 61 – 65 = –4
Consider the nth term of the A.P. as the first negative term
i.e., an < 0
We know that nth term of an AP,
an = a + (n – 1)d
Here, [a + (n – 1)d] < 0
Substituting the values
`\implies` 65 + (n – 1) (– 4) < 0
`\implies` 65 – 4n + 4 < 0
`\implies` 69 – 4n < 0
`\implies` 4n > 69
`\implies` `"n" > 69/4`
`\implies` n > 17.25
`\implies` n = 18
So the 18th term is the first negative term of the given AP.
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