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

If the difference between any two consecutive terms of a series is a constant value, then the series is an A.P

Given, the series is 2, 4, 8, 16, …
Here,
$a_{2} - a_{1} = 4 - 2 = 2$
$a_{3} - a_{2} = 8 - 4 = 4 a_{4} - a_{3} = 16 - 8 = 8$

Note that the difference between any two consecutive terms of the series is not a constant value.
Hence, the given series is not an AP.

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Q. 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 …

Question 4 (xii)
Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.
(xii) $\sqrt{2}, \sqrt{8}, \sqrt{18}, \sqrt{32} \dots \dots$

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) $a, a^{2}, a^{3}, a^{4}, \dots$