Question

164, 160, 156, 152, ...... are in Arithmetic Progression (A.P.). Find:

1. which term is equal to 0. 
2. the sum of its first 20 terms.

Answer 1

Here $$a = 164, \ d = -4$$. 

i. Let the nth term be 0:

$$164 + (n - 1)( - 4) = 0$$

$$\Rightarrow 168 - 4n = 0$$

$$\Rightarrow n = 42$$

So the 42nd term is 0. 

ii. $$S_{20} = \frac{20}{2}[2(164) + 19(-4)]$$

$$= 10(328 - 76)$$

$$= 2520$$