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Arithmetic Progressions — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsArithmetic Progressions2 Marks
Question
Is the given sequence: $a^1, a^2, a^3, a^4,...$ forms an AP? If it forms an AP, then find the common difference d and write the next three terms.
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Answer

Here, it is given that the exponent is increasing in each subsequent term:
$a_4= a^4, a_3= a^3, a_2= a^2, a_1= a^1$
$a_2- a_1= a^2- a^1$
$a_3- a_2= a^3- a^2$
$a_4- a_3= a^4- a^3$​​​​​​​
Since, the common difference is not same, since $a_{k+1}- a_k​​​​​​​$​​​​​​​ is not same for all values of k
Hence, the given sequence does not forms an AP. So,we can not find next three terms.

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