Question

if the six times the sixth term of an ap is eual to eleven times the eleventh term of same ap then find the seventeenth term

Answer 1

Hi

Here is ur answer

6th term = a + (6-1) d = a + 5d

11th term = a+ (11-1)d = a +10d

Given...

#  6 th term is 6 times  . So,  = 6 ( a +5d )

#  11th term is 11 times . So,  = 11 (a+10d)

Therefore,  

 It is given that both are equal,

6(a+5d) = 11(a +10d)

Multiply 6 and 11 inside.....

6a + 30d = 11a + 110d

Brind a oneside and d oneside

6a - 11a = 110d - 30d

- 5a = 80d

 a  = - 16d

Take -16d left hans side,

a + 16d = 0

Here,    $a + ( n-1) d = 0$

Therefore...

a + (17 - 1)d = 0

Hence,

17 th term is Zero

a 17 = 0

Hope it helps U