Question

Which of the following are APS? if they form an AP find the common difference d and write three more terms....(i)0.2,0.22,0.222,0.2222...
(ii)0,-4,-18,-12...(iii)-1/2,-1/2,-1/2,-1/2...

PLS GIVE PROPER ANSWER

Answer 1

GIVEN :

Which of the following is an APs . If yes then write more three terms otherwise no .

MAIN FACT :

If the common difference between APs series is same Only then it means It is APs ..

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SOLUTION :

(1) 0.2 , 0.22 , 0.222 ,.. 0.2222.......

Common difference => a2 - a1

=> 0.22 - 0.2

=> 0.02

=> 0.222 - 0.22

=> 0.002

This is shown that APs

0.2,0.22,0.222,0.2222....... is not an AP series because difference between series is not same .

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(2) 0 , -4 ,-8 ,-12 ........

=> a2 - a1

=> -4. - 0

=> -4

=> -8 -(-4)

=> -8 +4

=> -4

So this shown that 0 , -4 ,-8 ,-12. is Ap Series

So now next three terms are : .

=>. - 12 - 4

=> -16

=> -16 -4

=> -20

=> -20 - 4

=> -24

So the next three more terms are -16 , -20 , -24

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(3) -½ , -½ ,- ½ , -½ .......

$\frac{ - 1}{2} - \frac{ - 1}{2} \\ \\ \frac{ - 1}{2} + \frac{1}{2} \\ \\ = > \: 0$

Similarly all are same ,hence its also an APs ....

so next three terms are also the same ...

i.e -1/2 , -1/2 , -1/2 .....

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