Question

5 times the 5th term of an arithmetic progression is equal to 6 times the 6th term what is the value of 11th term

Answer 1

5 times the 5th term of an arithmetic progression is equal to 6 times the 6th term what is the value of 11th term

Answer 2

For the given arithmetic progression, the 11th term will be 0.

Given,

5 times the 5th term of an arithmetic progression is equal to 6 times the 6th term.

To find,

11th term.

Solution,

It can be seen that here, a relation between the 5th and 6th terms of an arithmetic progression or A. P.

That is,

5 times the 5th term = 6 times the 6th term.

Now, we know that the nth term of an A. P. is given as

$a_n=a+(n-1)d$

where,

$a_n$ = nth term,

a = first term,

d = common difference.

So, we can write the 5th term as

$a_5 = a+4d$

and, the 6th term can be written as

$a_6=a+5d$

Now, according to the given condition,

$5a_5=6a_6\\\implies 5(a+4d)=6(a+5d)$

⇒ 5a + 20d = 6a + 30d

Rearranging and simplifying the above equation, we get,

a = 20d - 30d

a = -10d.

Now, the 11th term can be found as

$a_{11}=a+10d$

Substitute the above-obtained value of 'a' in the above equation.

Since a = -10d, we obtain,

$a_{11}=(-10d)+10d$

$\implies a_{11}=0$

⇒ 11th term = 0.

Therefore, for the given arithmetic progression, the 11th term will be 0.

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