Write the value of a30 − a10 for the A.P. 4, 9, 14, 19, ....

In this problem, we are given an A.P. and we need to find $a_{30}-a_{10}$.

A.P. is $4,9,14,19 \ldots$

Here,

First term (a) = 4

Common difference of the A.P. (d) 

Now, as we know,

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

Here, we find $a_{30}$ and $a_{20}$.

So, for $30^{\text {th }}$ term,

$a_{30}=a+(30-1) d$

$=4+(29)(5)$

$=4+145$

$=149$

Also, for $10^{\text {th }}$ term,

$a_{20}=a+(10-1) d$

$=4+(9)(5)$

$=4+45$

$=49$

So,

$a_{30}-a_{10}=149-49$

$=100$

Therefore, for the given A.P $a_{30}-a_{10}=100$.