Question

The sum of how many terms of the A.P 22, 20, 18, … will be zero?

Answer 1

We’ll put the values of the first term, common difference of the A.P in the formula of the sum of an A.P and find the value of the number of terms by equating it to 0.

Complete step-by-step answer:
Given, the sequence 22, 20, 18, …
Here the first term $a = 22$ and the common difference $d = 20 - 22 = - 2$
The sum of an A.P is given by ${S_n} = \dfrac{n}{2}\left( {2a + (n - 1)d} \right)$

$$\Rightarrow 0 = \dfrac{n}{2}\left( {2 \times 22} \right) + (n - 1)( - 2)) \\\ \Rightarrow n(46 - 2n) = 0 \\\$$

Now $n \ne 0$

$$\Rightarrow n = \dfrac{{46}}{2} \\\ \Rightarrow n = 23 \\\$$

Therefore, the sum of 23 terms of the A.P 22, 20, 18, … will be zero

Note: In case the question had been asked about the term at which the sum of the A. P terminates to 0, then in that case one should use the relation between the sum of an A.P and the last term of the A.P.