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  • Justify whether it is true to say that the following are the nth terms of an AP. 3n^2+5

Justify whether it is true to say that the following are the nth terms of an AP.

3n^2+5

Answers (1)

Answer.          [No]

Solution.        

\text{Here}, \( a_n = 3n^2 + 5 \)\\ \text{Put }\( n = 1 \), \( a_1 = 3(1)^2 + 5 = 3 + 5 = 8 \)\\ \text{Put }\( n = 2 \), \( a_2 = 3(2)^2 + 5 = 12 + 5 = 17 \)\\ \text{Put }\( n = 3 \), \( a_3 = 3(3)^2 + 5 = 27 + 5 = 32 \)\\ \text{Numbers are: }8, 17, 32 $\ldots$ \\ \( a_2 - a_1 = 17 - 8 = 9 \)\\ \( a_3 - a_2 = 32 - 17 = 15 \)

Here common difference is not the same

Therefore series 3n^2+5 is not the nth term of an AP.

 

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infoexpert21

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