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In an AP if a_2 = 13; a_4 = 3 find a_1, a_3

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

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James Discussed

In an AP if

a_{2} = 13;

a_{4} = 3

find

a_{1}, a_{3}

8 mins ago

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8 mins ago

Text solutionVerified

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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