Question 8 (ii)
Justify whether it is true to say that the following are the nth terms of an AP.
$3 n^{2} + 5$

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Solution

$G i v e n, a_{n} = 3 n^{2} + 5$
$P u t n = 1, a_{1} = 3 (1)^{2} + 5 = 8$
$P u t n = 2, a_{2} = 3 (2)^{2} + 5 = 3 (4) + 5 = 17$
$P u t n = 3, a_{3} = 3 (3)^{2} + 5 = 3 (9) + 5 = 27 + 5 = 32$
So, the series is :
8, 17, 32, ...

Here,
$a_{2} - a_{1} = 17 - 8 = 9$
$a_{3} - a_{2} = 32 - 17 = 15$
$a_{2} - a_{1} \neq a_{3} - a_{2}$
Since the difference between the consecutive terms of the series is not same, the formula does not represent the nth term of an AP.

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