The 19th term of an AP is equal to 3 times its 6 term. If its 9th term is 19, find the AP.
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a+8d=19........(1)
a+18d=3(a+5d)
a+18d=3a+15d
a+18d-3a-15d=0
-2a+3d=0
2a-3d=0..........(2)
a+8d=19 ×(2)
2a-3d=0 ×(1)
2a+16d=38
2a- 3d =0
- + -
__________
19d=38
d=2
2a-3d=0
2a-3(2)=0
2a-6=0
2a=6
a=3
3,5,7.........A.P.
a+18d=3(a+5d)
a+18d=3a+15d
a+18d-3a-15d=0
-2a+3d=0
2a-3d=0..........(2)
a+8d=19 ×(2)
2a-3d=0 ×(1)
2a+16d=38
2a- 3d =0
- + -
__________
19d=38
d=2
2a-3d=0
2a-3(2)=0
2a-6=0
2a=6
a=3
3,5,7.........A.P.
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