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nth Term of A.P

In an AP if ...

Question

In an AP if $a_{2} = 13;$ $a_{4} = 3$ find $a_{1}, a_{3}$

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Solution

Given AP
$a_{2} = 13$ $a_{4} = 3$
$a_{2} = a + (n - 1) d = a + d$
$a_{4} = a + (4 - 1) d = a + 3 d$
Here $a + d = 13$ (1)
$a + 3 d = 3$ (2)
(2) - (1) $\Rightarrow 2 d = - 10$
$d = - 5$
substitute d= -5 in (1)
a-5 = 13
a = 18
$∴ a_{1} = a = 18$
$a_{3} = a + 2 d = 18 + 2 (- 5)$
$= 8$

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