Question 4 (xi)
Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.
(xi) $a, a^{2}, a^{3}, a^{4} \dots \dots$

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Solution

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

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Question 4 (xi) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (xi) a,a2,a3,a4……

(xi) a,a2,a3,a4……Here,a2−a1=a2−a=(a−1)a3−a2=a3−a2=a2(a−1)a4−a3=a4−a3=a3(a−1)⇒an+1−an is not the same everytime. Therefore, the given numbers are not forming an A.P.

Question 4 (xi)
Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.
(xi) $a, a^{2}, a^{3}, a^{4} \dots \dots$