How many terms of the sequence $18, 16, 14, . . . .$ should be taken so that their sum is zero?

19

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17

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18

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16

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Solution

The correct option is C $19$
Here $a = 18, d = - 2$ .
Let there are $n$ terms so that the sum is zero.
Now, $S_{n} = \frac{n}{2} [2 a + (n - 1) d] = 0$
$\Rightarrow \frac{n}{2} [2 \times 18 + (n - 1) \times - 2] = 0$
$\Rightarrow 36 + (n - 1) \times - 2 = 0$
$\Rightarrow n - 1 = 18$
$\Rightarrow n = 19$
Therefore $19$ terms of the sequence has to be taken so that their sum is zero.

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Similar questions

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(i) How many terms of the sequence $18, 16, 14, . . .$ should be taken so that their sum is zero?
(ii) How many terms are there in the A.P. whose first and fifth terms are $- 14$ and $2$ respectively and the sum of the terms is $40$ ?
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Q. (i) How many terms of the sequence 18, 16, 14, ... should be taken so that their sum is zero?

(ii) How many terms are there in the A.P. whose first and fifth terms are −14 and 2 respectively and the sum of the terms is 40?

(iii) How many terms of the A.P. 9, 17, 25,... must be taken so that their sum is 636?

(iv) How many terms of the A.P. 63, 60, 57, ... must be taken so that their sum is 693?

(i) How many terms of the sequence $18, 16, 14, . . .$ should be taken so that their sum is zero?
(ii) How many terms are there in the A.P. whose first and fifth terms are $- 14$ and $2$ respectively and the sum of the terms is 40?
(iii) How many terms of the A.P., $9, 17, 25, . . .$ must be taken so that their sum is $636$ ?
(iv) How many terms of the A.P., $63, 60, 57, . . .$ must be taken so that their sum is $693$ ?
(v) How many terms of the A.P., $27, 24, 21...$ should be taken so that their sum is zero?
(vi) How many terms of the A.P., $45, 39, 33...$ must be taken so that their sum is $180$ ?

Q. How many terms of sequence

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. Also explain the reason of double answers.

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How many terms of the sequence 18,16,14,.... should be taken so that their sum is zero?

The correct option is C 19Here a=18,d=−2.Let there are n terms so that the sum is zero.Now, Sn=n2[2a+(n−1)d]=0⇒n2[2×18+(n−1)×−2]=0⇒36+(n−1)×−2=0⇒n−1=18⇒n=19Therefore 19 terms of the sequence has to be taken so that their sum is zero.

How many terms of the sequence $18, 16, 14, . . . .$ should be taken so that their sum is zero?