Question

The 19th term of an ap is equal to 3 times its6th term.if its 9th is 19 .find the ap

Answer 1

let in anAP first term =a, Common difference =d

9th term =19

a+8d=19----(1)

19th term =3*(6th term)

a+18d=3(a+5d)

a+18d=3a+15d

0=3a+15d-a-18d

2a-3d=0---(2)

subtract (2) from 2*(1)

-19d=-38

d=2

substitute d=2 in (1)

a=3

therefore

a=3,d=2

required AP is

3,5,7,9,....

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