Question

Question from Aritmetic and Geometric Progressions

How many terms of the A.P. 27, 24, 21,.......should be taken so that their sum is zero?

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Answer 1

Given Series is 27,24, 21...

Here, a = 27.

Common difference d = 24 - 27 = -3.

Sum = sn = 0.

We know that Sum of n terms of an AP sn = (n/2)[2a + (n - 1) * d]

⇒ 0 = (n/2)[2(27) + (n - 1) * (-3)]

⇒ 0 = n[54 - 3n + 3]

⇒ 0 = n[57 - 3n]

⇒ 57n - 3n^2 = 0

⇒ n(57 - 3n) = 0

⇒ 57 - 3n = 0

⇒ 57 = 3n

⇒ n = 19

So, the number of terms is 19.

Hope it helps!

Answer 2

Let Sn be 0

a=27 , d=-3

we know that,

Sn= n/2[2a+(n-1)d]

0=n/2[2×27+(n-1)-3]

0×2=n[54-3n+3]

0=n[57-3n]

0=-3n²+57n

0=-3n(n-19)

0/-3n=n-19

0=n-19

19=n

Hence ,No. of 19 terms should taken so that sum of given AP is 0

Hope this helps u...

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