Question

The 19th term of an ap is equal to 3 times its 6th if its 9th term is 1900 find the ap

Answer 1

Answer:

AP: 300, 500, 700, 900, 1100

Step-by-step explanation:

19th term = 3× 6th term

=> a19 = 3× a6

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

=> a+18d = 3a+ 15d

=> 2a= 3d

=> a= 3/2d - - - - - - - (1)

Now,

9th term =1900

=> a9 = 1900

=> a+8d = 1900

=> 3/2d +8d = 1900 [ from(1)]

=>3d + 16d/2 =1900

=>19d = 1900 ×2

=> d= 200 - - - - - - - - (2)

In eq (1),

a=3/2 d

=> a= 3/2 × 200 [from (2)]

=> a= 300

Now, a=300 and d=200

So, AP: a, a+d, a+2d, a+3d, a+4d....

=> AP: 300, 300+200, 300+400, 300+600, 300+800...

=> AP: 300, 500, 700, 900, 1100...

Thank you

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