Question

the sum of 6th and 9th term of an. AP is 30 and the sum of the 4th and 8th term is 24 .find the first three term of AP​

Answer 1

The sum of 6th and 9th term of an AP is 30

$\boxed{a6 + a9 = 30}.....(1)$

The sum of 4th and 8th term is 24

$\boxed{a4 + a8 = 24}.....(2)$

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From (1)

$a6 = > a + 5d \\ \\ a9 = > a + 8d$

put the values in (1)

$a + 5d + a + 8d = 30 \\ \\ 2a + 13d = 30........(3)$

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From(2)

$a4 = > a + 3d \\ \\ a8 = > a + 7d$

Put the values in (2)

$a + 3d + a + 7d = 24 \\ \\ 2a + 10d = 24..........(4)$

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By elimination method

$2a + 13d = 30 \\ \frac{2a + 10d = 24}{ } \\ \frac{ - \: \: \: \: \: - \: \: \: \: \: \: \: \: - \: \: }{3d = 6 } \\ \\ d = \frac{6}{3} \\ \\d = > 2$

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Put Value of d in equation (4)

$2a + 10(2) = 24 \\ 2a + 20 = 24 \\ 2a = 24 - 20 \\ 2a = 4 \\ a = \frac{4}{2 } \\ \\a = > 2$

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Ap series

=> a,(a+d),(a+2d),(a+3d),........................(a+nd)

put the values of a and d in Ap series .

1st term(a)=> 2

2nd term(a+d)

=> 2+2

=>4

3rd term(a+2d)

=>2+2(2)

=>2+(4)

=>6

So first three terms of Ap series are .......

2,4,6,8...............

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Hope it's helps u ☺️

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Thnkx☺️