How many terms of an AP 27- 24- 21- - are required to get the sum as 0- 27-19 nbsp-17-24-

The correct option is B 19 nbsp; Given that nbsp;AP is 27, 24, 21 … a = 27; d = 24 27 = 3 S_n = nbsp;n/2 ( 2a + ( n 1) d) Since the sum is 0 ⇒n/2 [ ...

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Standard VIII

Mathematics

Sum of first n natural numbers

How many term...

Question

How many terms of an AP 27, 24, 21, ... are required to get the sum as 0?

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Solution

The correct option is B
19

Given that AP is 27, 24, 21 …
a = 27; d = 24 - 27 = -3

$S_{n} = \frac{n}{2} (2 a + (n - 1) d)$

Since the sum is 0

$\Rightarrow \frac{n}{2} [2 \times 27 + (n - 1) (- 3)] = 0$

$\Rightarrow n (54 - 3 n + 3) = 0$

$\Rightarrow n (57 - 3 n) = 0$

$\Rightarrow n = 0 a n d 57 - 3 n = 0$

$∴ n = 0 a n d n = 19$

Since the number of terms cannot be equal to 0, so n = 19.

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How many terms of an AP 27, 24, 21, ... are required to get the sum as 0?

The correct option is B 19 Given that AP is 27, 24, 21 … a = 27; d = 24 - 27 = -3 Sn=n2(2a+(n−1)d) Since the sum is 0 ⇒n2[2×27+(n−1)(−3)]=0 ⇒ n(54−3n+3)=0 ⇒ n(57−3n)=0 ⇒n=0 and 57−3n=0 ∴n=0 and n=19 Since the number of terms cannot be equal to 0, so n = 19.