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