Question

The 19th term of an ap is equal to three times its 6th term. if the 9th term is 19 then a = ?

Answer 1

Answer:

a=3

Step-by-step explanation:

let 1st term = a and common difference = d

19th term = t19 = a + 18d

6th term = t6 = a + 5d

9th term = t9 = a + 8d = 19 (given)

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

also given,

t19 = 3×t6

=> a + 18d = 3×(a + 5d) = 3a + 15d

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

=> 2a - 3d = 0

=> 2(19 - 8d) - 3d = 0 [from (1)]

=> 38 - 16d - 3d = 0

=> 19d = 38

=> d = 38/19 = 2

putting d in (1),

a = 19 - 8d = 19 - 8×2 = 3