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# Is it an AP or arithmetic progression?1, 4, 7, 10, 13, 16, 19, 22, 25 …(A). Yes (B). No(C). Ambiguous(D). Data insufficient

Last updated date: 14th Jul 2024
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Hint: The formula for writing ${{n}^{th}}$ term of an arithmetic progression is
${{n}^{th}}\ term=a+(n-1)d$
(Where ‘a’ is the first term and‘d’ is the common difference of the arithmetic progression)
We can find that the given series is an arithmetic progression by firstly assuming that the given series is an arithmetic progression. Then if the series follows the rules of an arithmetic progression, then we can conclude that the given is an arithmetic progression.

Now, as given in the hint, if the above series follows the formula for writing ${{n}^{th}}$ term of an arithmetic progression, then, we can say that it is actually an arithmetic progression.
${{n}^{th}}\ term=a+(n-1)d$
\begin{align} & {{9}^{th}}\ term=1+(9-1)3 \\ & 25=1+8\times 3 \\ & 25=1+24 \\ & 25=25 \\ \end{align}
Note: The students can make an error in writing the sum and ${{n}^{th}}$ term if they might confuse in finding the common difference that is ‘d’ as the value of ‘d’ would be found only on proceeding with the question by taking the common difference as an unknown variable.