Question

if the ratio of the 10th term and 21th term of an ap is 5:16 which term of the ap will be equal to 0

pls answer only if u know​

Answer 1

Solution:

Let us assume that:

$\rm \longrightarrow a = First \: Term \: of \: AP$

$\rm \longrightarrow d = Common \: Difference\: of \: AP$

$\rm \longrightarrow a_{n}= n^{th} \: Term \: of \: AP$

We know that:

$\rm \longrightarrow a_{n}= a + (n - 1)d$

Now, it's given that:

$\rm \longrightarrow \dfrac{a_{10}}{a_{21}} = \dfrac{5}{16}$

On cross multiplying, we get:

$\rm \longrightarrow 16 \: a_{10} = 5 \: a_{21}$

$\rm \longrightarrow 16(a + 9d)= 5(a + 20d)$

$\rm \longrightarrow 16a + 144d = 5a +100d$

$\rm \longrightarrow (16 - 5)a=(100 - 144)d$

$\rm \longrightarrow 11a= - 44d$

$\rm \longrightarrow a= - 4d$

$\rm \longrightarrow a + 4d = 0$

$\rm \longrightarrow a + (5 - 1)d = 0$

Therefore:

$\rm \longrightarrow a_{5} = 0$

★ So, the fifth term of the given AP is 0.

Answer:

• The fifth term of the given AP is zero.

Answer 2

Solution:

Let us assume that:

a = First Term of AP

d = Common Difference of AP

$a_{n}= n^{th} \: Term \: of \: AP$

We know that:

$a_{n}= a + (n - 1)d$

Now, it's given that:

$\rm \longrightarrow \dfrac{a_{10}}{a_{21}} = \dfrac{5}{16}$

On cross multiplying, we get:

$16 \: a_{10} = 5 \: a_{21}$

$16 ( a + 9d ) = 5 ( a + 20d ) \\ \\ 16a + 144d = 5a + 100d \\ \\ (16 −5)a=(100−144) \\ \\ 11a=−44d \\ \\ a=−4d \\ \\ a+4d=0 \\ \\ a+(5−1)d=0$

Therefore:

$a_{5} = 0$

So, the fifth term of the given AP is 0.