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

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Solution

No.
Here, $a_{n}$ = 1+n+ $n^{2}$
$P u t n = 1, a_{1} = 1 + 1 + (1)^{2} = 3$
$P u t n = 2, a_{2} = 1 + 2 + (2)^{2} = 1 + 2 + 4 = 7$
$P u t n = 3, a_{3} = 1 + 3 + (3)^{2} = 1 + 3 + 9 = 13$
The numbers are;
3, 7, 13, ...
Here, $a_{2} - a_{1} = 7 - 3 = 4$
$a_{3} - a_{2} = 13 - 7 = 6$
$a_{2} - a_{1} \neq a_{3} - a_{2}$
Since the successive difference of the numbers is not same, it does not form an AP.

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