Question

If 5times of 6th term of an Ap is equal to the 6 time the 7th,then the 12th term of the Ap is

Answer 1

Step-by-step explanation:

the question seems to be incomplete plz give full questions

Answer 2

Answer

$\mathtt{12th\:\: term\:\: i.e\:\: a_{12}\:= 0}$

Explaination

$\text{\underline{Given}}$

$\mathtt{5a_{6} = 6a_{7}\: \rightarrow (1)}$

$\mathtt{To\: find\: : a_{12}}$

$\text{\underline{\underline{Solution}}}$

$\mathtt{\implies\: a_{6} = a + 5d \:\rightarrow (2)}$

$\mathtt{\implies\: a_{7} = a + 6d\:\rightarrow (3)}$

From eqn (1)

$\mathtt{5a_{6} = 6a_{7}\:}$

$\text{Using (2) and (3) }$

$\mathtt{\implies\: 5(a + 5d) = 6(a + 6d)}$

$\mathtt{\implies\: 5a + 25d = 6a + 36d}$

$\mathtt{\implies\: a = -11d \:\rightarrow (4)}$

Now,

$\mathtt{\implies\: a_{12} = a + 11d}$

$\mathtt{\implies\: a_{12} = -11d + 11d\:\rightarrow {Using (4)} }$

$\mathtt{\implies\: a_{12} = 0}$