Question

if t10-t5=200 then the comman differece is?
Give step by step explaination. Please ​

Answer 1

ANSWER:

Given:

• $t_{10}-t_{5}=200$

To Find:

• Common difference

Solution:

We are given that,

$\implies t_{10}-t_{5}=200$

We know that,

$\hookrightarrow t_n=a+(n-1)d$

Here, a is first term and d is the common difference.

So,

$\implies t_{10}=a+(10-1)d$

$\implies t_{10}=a+9d$

Similarly,

$\implies t_5=a+(5-1)d$

$\implies t_5=a+4d$

We had,

$\implies t_{10}-t_{5}=200$

So,

$\implies (a+9d)-(a+4d)=200$

$\implies a\!\!\!/+9d-a\!\!\!/-4d=200$

$\implies 5d=200$

So,

$\implies d=\dfrac{200\!\!\!\!\!/}{5\!\!\!/}$

Hence,

$\implies\bf d=40$

Therefore, common difference is 40.