39. The 19th term of an AP is equal to 3 times its 6th term. If its 9t

1.	39. The 19th term of an AP is equal to 3 times its 6th term. If its 9th termICBSE 2019, find the AP.
Answer» Let in anAP first term =a, Common difference =d9th term =19a+8d=19----(1)19th term =3(6th term)a+18d=3(a+5d)a+18d=3a+15d0=3a+15d-a-18d2a-3d=0---(2)subtract (2) from 2(1)-19d=-38d=2substitute d=2 in (1)a=3thereforea=3,d=2required AP is3,5,7,9,.... Solution: a19= a+18d andIt is 3times the 6term So, a+18d=3(a+5d) a+18d=3a + 15d Subtract 3a-a=18d- 15d 2a-3d -3d=-2a d= -2a/-3 or 2a/3 Put this value in the below equation as we have , a9= a+8d= 19 a+ 8× 2a/3=19 a+ 16a/3= 19 (3a+ 16a)/3=19 19a/3=19 19a= 19×3 a= 57/19=3 D=2a/3=. 2×3/3=2 So the AP will be 3,5,7,9, 11....….

39. The 19th term of an AP is equal to 3 times its 6th term. If its 9th termICBSE 2019, find the AP.

Answer»

Let in anAP first term =a, Common difference =d9th term =19a+8d=19----(1)19th term =3*(6th term)a+18d=3(a+5d)a+18d=3a+15d0=3a+15d-a-18d2a-3d=0---(2)subtract (2) from 2*(1)-19d=-38d=2substitute d=2 in (1)a=3thereforea=3,d=2required AP is3,5,7,9,....

Solution:

a19= a+18d andIt is 3times the 6term So, a+18d=3(a+5d) a+18d=3a + 15d Subtract 3a-a=18d- 15d 2a-3d -3d=-2a d= -2a/-3 or 2a/3 Put this value in the below equation as we have , a9= a+8d= 19 a+ 8× 2a/3=19 a+ 16a/3= 19 (3a+ 16a)/3=19 19a/3=19 19a= 19×3 a= 57/19=3 D=2a/3=. 2×3/3=2

So the AP will be 3,5,7,9, 11....….

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