Question

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

Answer 1

9 th term of an AP = 6 * 2nd term

a + ( 9 - 1 ) d = 6 ( a + ( 2 - 1 ) d

a + 8d = 6 ( a + d)

a + 8d = 6a + 6d

8d - 6d = 6a - a

2d = 5a

d = 5/2 a

nw its given tat 5th term is 22

so,.....

22 = a + (n-1)d

22 = a + ( 5 - 1)d

22 = a + 4d

22 = a + 4 (5/2 a ) (the value which we found above for d )

22 = a + 2 * 5 a ( 4 and 2 will get cancelled)

22 = a + 10 a

22 = 11a

a = 2

d =5/2 a

d = 5/2*2

d = 5

nw the AP is: 2,7.12,17,22,27.

Hope it helps you.