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Arithmetic Progressions — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsArithmetic Progressions3 Marks
Question
Is the given series $2, 4, 8, 16, ......$ form an $AP$? If It forms an $AP$, then find the common difference d and write the next three terms. 
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Answer

If $a_{k+1}- a_k$is same for different values of k, then the series is in the form of an AP.
here, we have $a_1= 2, a_2= 4, a_3= 8$ and $a_4 = 16$
$a_4- a_3 = 16 - 8 = 8$
$a_3- a_2 = 8 - 4 = 4$
$a_2- a_1= 4 - 2 = 2$
$Here, $a_{k+1}- a_k$_ i.e. the common difference is not same for all values of k
Hence, the given series does not form an AP.

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