Question

If seven times the 7^th term of an A.P. is equal to eleven times the 11^th term, then what will be its 18^th term?

Answer 1

Given: seven times the 7^th term of an A.P. is equal to eleven times the 11^th term

nth term of an AP given by 

\[a + \left( n - 1 \right)d = a_n\]

Thus, the 7th term will be

\[a_7 = a + \left( 7 - 1 \right)d\]
\[ \Rightarrow a_7 = a + 6d . . . \left( 1 \right)\]

 the 11th term will be

\[a_{11} = a + \left( 11 - 1 \right)d\]

\[ \Rightarrow a_{11} = a + 10d . . . \left( 2 \right)\]

Now,

\[7\left( a + 6d \right) = 11\left( a + 10d \right)\]

\[\Rightarrow 7a + 42d = 11a + 110d\]

\[ \Rightarrow 11a - 7a + 110d - 42d = 0\]

\[ \Rightarrow 4a + 68d = 0\]

\[ \Rightarrow 4\left( a + 17d \right) = 0\]

\[ \Rightarrow \left( a + 17d \right) = 0\]

So, the 18th term is 0.