an important question from the book -ML aggarwal( avichal publication)class 10th , chapter9, Arithmetic Progression……..
Which term of the AP 53, 48, 43…..is the first negative term?
Class10, Chapter9, Arithemtic Progression, ML Publication
Which term of the AP 53, 48, 43…..is the first negative term?
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Here first term a=53 and common difference d=−5
Let nth term is the first negative term of the given AP.
Therefore,
nth term in AP = a + (n – 1)*d
= 53 + (n -1)*(- 5)
= 53 – 5n + 5
= 53 + 5 – 5n
= 58 – 5n
Now, we have to find the suitable value of n, so that the value of (58 – 5n) is negative.
Let us take n = 11
nth term = 58 – (5*11)
= 58 – 55
= 3 Which is not negative.
Then putting n = 12, we get.
nth term = 58 – (5*12)
= 58 – 60
= – 2
This is the first negative term of the series, and it is the 12th term of the AP.
So, n =12