Are $2, 4, 8, 16, \ldots$ in an $AP$? If they form an $AP$,find the common difference $d$ and write three more terms.
(N/A) Given sequence: $2, 4, 8, 16, \ldots$
To check if the sequence is an $AP$,we calculate the difference between consecutive terms:
$a_2 - a_1 = 4 - 2 = 2$
$a_3 - a_2 = 8 - 4 = 4$
$a_4 - a_3 = 16 - 8 = 8$
Since the difference between consecutive terms $(a_{k+1} - a_k)$ is not constant,the given sequence does not form an $AP$.
To check if the sequence is an $AP$,we calculate the difference between consecutive terms:
$a_2 - a_1 = 4 - 2 = 2$
$a_3 - a_2 = 8 - 4 = 4$
$a_4 - a_3 = 16 - 8 = 8$
Since the difference between consecutive terms $(a_{k+1} - a_k)$ is not constant,the given sequence does not form an $AP$.
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