Question 4 (i)
Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.
(i) 2, 4, 8, 16 …

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Solution

(i) 2, 4, 8, 16 …
Here, $a_{2} - a_{1} = 4 - 2 = 2 a_{3} - a_{2} = 8 - 4 = 4 a_{4} - a_{3} = 16 - 8 = 8 \Rightarrow a_{n + 1} - a_{n} i s n o t s a m e f o r a l l v a l u e s o f n .$
$H e n c e, t h e g i v e n s e r i e s i s n o t a n A P .$

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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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Q. Question 4 (vi)
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Question 4 (xi)
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Q. Question 4 (xv)
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 (i) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (i) 2, 4, 8, 16 …

(i) 2, 4, 8, 16 … Here, a2−a1=4−2=2a3−a2=8−4=4a4−a3=16−8=8⇒an+1−an is not same for all values of n. Hence, the given series is not an AP.

Question 4 (i)
Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.
(i) 2, 4, 8, 16 …

(i) 2, 4, 8, 16 …
Here, $a_{2} - a_{1} = 4 - 2 = 2 a_{3} - a_{2} = 8 - 4 = 4 a_{4} - a_{3} = 16 - 8 = 8 \Rightarrow a_{n + 1} - a_{n} i s n o t s a m e f o r a l l v a l u e s o f n .$
$H e n c e, t h e g i v e n s e r i e s i s n o t a n A P .$