Question 4 (vi)
Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.
(vi) 0.2, 0.22, 0.222, 0.2222 ….

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Solution

(vi) $0.2, 0.22, 0.222, 0.2222 \dots \dots H e r e, a_{2} - a_{1} = 0.22 - 0.2 = 0.02 a_{3} - a_{2} = 0.222 - 0.22 = 0.002 a_{4} - a_{3} = 0.2222 - 0.222 = 0.0002 \Rightarrow a_{n + 1} - a_{n} i s n o t t h e s a m e e v e r y t i m e .$
Therefore, the given numbers are not forming an A.P.

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Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.
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Question 4 (vi) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (vi) 0.2, 0.22, 0.222, 0.2222 ….

(vi) 0.2,0.22,0.222,0.2222……Here,a2−a1=0.22−0.2=0.02a3−a2=0.222−0.22=0.002a4−a3=0.2222−0.222=0.0002⇒an+1−an is not the same everytime. Therefore, the given numbers are not forming an A.P.

Question 4 (vi)
Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.
(vi) 0.2, 0.22, 0.222, 0.2222 ….

(vi) $0.2, 0.22, 0.222, 0.2222 \dots \dots H e r e, a_{2} - a_{1} = 0.22 - 0.2 = 0.02 a_{3} - a_{2} = 0.222 - 0.22 = 0.002 a_{4} - a_{3} = 0.2222 - 0.222 = 0.0002 \Rightarrow a_{n + 1} - a_{n} i s n o t t h e s a m e e v e r y t i m e .$
Therefore, the given numbers are not forming an A.P.