9th term of ap is 19 . 19th term of ap is equal to 3 tines the 6th term
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9th term is = a + (9-1) d=> 19= a+8d .. eq.1
19th term is 3 times 6th term so 3{a +(6-1)d}= a+ (19-1)d => 3a+ 15d = a+18d => 3a-a=18d-15d => 2a=3d so a = 3/2d
Putting this in eq1 so
3/2d +8d = 19
(3d + 16d)/2 = 19
19d= 19x2
19d = 38
D= 2
So d = 2 then putting this in eq1 19=a+8d
19= a + 8x2
19= a + 16
19-16=a
a= 3 now by a=3 and d = 2 u can find any term
19th term is 3 times 6th term so 3{a +(6-1)d}= a+ (19-1)d => 3a+ 15d = a+18d => 3a-a=18d-15d => 2a=3d so a = 3/2d
Putting this in eq1 so
3/2d +8d = 19
(3d + 16d)/2 = 19
19d= 19x2
19d = 38
D= 2
So d = 2 then putting this in eq1 19=a+8d
19= a + 8x2
19= a + 16
19-16=a
a= 3 now by a=3 and d = 2 u can find any term
Answered by
1
19=a+8d (equation 1)
a+18d=3(a+5d)
a+18d=3a+15d
3a-a=18d-15d
2a=3d
a=3d/2 (substitute in equation 1)
19=3d/2+8d
19=3d/2+16d/2 (transpose 2 to other side)
19*2=19d
38=19d
d=38/19
d=2
a=3d/2
a=3*2/2
a=3
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