Question

the 19th term of an ap is equal to 6 time its 6th term ninth term is 19 find the AP​

Answer 1

Answer:

Step-by-step explanation:

Given The 19th term of an ap is equal to 3 times its 6th term and ninth term is 19 find the AP

Let a be the first term and d will be the common difference.

Now given a19 = 3 a6

    So a + 18 d = 3(a + 5d) (an = a + (n-1)d)

     a + 18d = 3a + 15d

2a =  3d---------- 1

Also a9 = 19

a + 8d = 19----------2

From 1 and 2 we get

3d/2 + 8d = 19

19d = 38

 d = 2

Put d = 2 in 1 we get

2a = 3 x 2

  a = 3

Now a2 = a + d = 3 + 2 = 5

        a 3 = a + 2d = 3 + 2 x 2 = 7

The AP will be 3,5,7,9……