In an AP five times of $5^{th}$ term is equal to ten times the $10^{th}$ term, show that its 15th term is zero.

Given: In an AP five times of $5^{th}$ term is equal to ten times the $10^{th}$ term.

To do: To show that its $15^{th}$ term is zero.

Solution:

$5^{th}$ Term $=a+4d$

$10^{th}$ Term $=a+9d$

According to question,

$5(a+4d) = 10(a+9d)$

$\Rightarrow 5a+20d = 10a+90d$

$\Rightarrow 10a+90d-5a-20d =0$

$\Rightarrow 5a+70d =0$

$\Rightarrow 5( a+14d) =0$

$\Rightarrow a+14d =\frac{0}{5}$

$\Rightarrow a+14d =0$

Which is $15^{th}$ Term.

Hence Proved.

Updated on: 10-Oct-2022

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