the 19th term of an ap is equal to 3 times its 6 term if its 9 term is 19 find the AP
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a= 3 and c.d = 2 this is the answer which I have done.... see the picture
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noblekahuna15627:
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a19=3×a6---(1)
&
a9=19----(2)
from(1)
a+18d=3×(a+5d)
a+18d=3a+15d
2a=3d
a=3d/2----(3)
from(2)
a+8d=19
3d/2+8d=19. (from 3)
3d+16d/2=19
3d+16d=38
19d=38
d=38/19
d=2
put value of ''d''in (3)
a=3×2/2
a=3
a2=3+2=5
a3=3+2×2=7
a4=3+3×2=9
AP:3,5,7,9,..
&
a9=19----(2)
from(1)
a+18d=3×(a+5d)
a+18d=3a+15d
2a=3d
a=3d/2----(3)
from(2)
a+8d=19
3d/2+8d=19. (from 3)
3d+16d/2=19
3d+16d=38
19d=38
d=38/19
d=2
put value of ''d''in (3)
a=3×2/2
a=3
a2=3+2=5
a3=3+2×2=7
a4=3+3×2=9
AP:3,5,7,9,..
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