Question

find the ap whoose 4th term 9 and 6th and 13th term 40

Answer 1

Answer:

a4 = 9

a + 3d = 9_____eq i

a6 + a13 = 4

a+5d + a+12d = 40a

2a + 17d = 40______eq ii

by using elimination method...

a + 3d = 9____eq i

2a + 17d = 40___eq ii

multiply the equation i by 2...

2a + 6d = 18____eq i

2a + 17d = 40____eq ii

(change the signs of equation ii...)

-2a - 17d = - 40

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0 - 11d = - 22

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11d = 22

d = 22/11

d = 2

put the value of d in eq i

a + 3d = 9

a + 3(2) = 9

a = 9 - 6

a = 3

we know the general form of AP...

a , a+d , a+2d , a+3d

a = 3

a+d = 3+2 = 5

a+2d = 3+2(2) = 7

a+3d = 3+3(2) = 9

AP...3,5,7,9

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