Find the $12^{t h}$ , $24^{t h}$ and $n^{t h}$ term of the A.P. given by 9, 13, 17, 21, 25, .........

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Solution

We have,

a = First term = 9 and,

d = Common difference = 4 [Since, 13 – 9 = 4, 17 – 13 = 4, 21 – 7 = 4 etc.]

We know that the $n^{t h}$ term of an A.P. with first term a and common difference d is given by

$a_{n} = a + (n - 1) d$

Therefore,

$a_{12} = a + (12 - 1) d$

$= a + 11 d$

$= 9 + 11 \times 4$

$= 53$

$a_{24} = a + (24 - 1) d$

$= a + 23 d$

$= 9 + 23 \times 4$

$= 101$

and,

_{$a_{n}$} = a + (n – 1) d

$= 9 + (n - 1) \times 4 = 4 n + 5$

$a_{12}$ = 53, $a_{24}$ = 101 and $a_{n}$ = 4n + 5

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