Question 4 (ix)
Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.
(ix) 1, 3, 9, 27 …

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Solution

(ix) $1, 3, 9, 27 \dots \dots H e r e, a_{2} - a_{1} = 3 - 1 = 2 a_{3} - a_{2} = 9 - 3 = 6 a_{4} - a_{3} = 27 - 9 = 18 \Rightarrow a_{n + 1} - a_{n} i s n o t t h e s a m e e v e r y t i m e .$
Therefore, the given numbers are not forming an A.P.

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Question 4 (ix) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (ix) 1, 3, 9, 27 …

(ix) 1,3,9,27……Here,a2−a1=3−1=2a3−a2=9−3=6a4−a3=27−9=18⇒an+1−an is not the same everytime. Therefore, the given numbers are not forming an A.P.

Question 4 (ix)
Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.
(ix) 1, 3, 9, 27 …

(ix) $1, 3, 9, 27 \dots \dots H e r e, a_{2} - a_{1} = 3 - 1 = 2 a_{3} - a_{2} = 9 - 3 = 6 a_{4} - a_{3} = 27 - 9 = 18 \Rightarrow a_{n + 1} - a_{n} i s n o t t h e s a m e e v e r y t i m e .$
Therefore, the given numbers are not forming an A.P.