Question:
Write the value of $a_{30}-a_{10}$ for the A.P. $4,9,14,19, \ldots .$
Solution:
In this problem, we are given an A.P. and we need to find.
A.P. is
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 a30 and a20.
So, for 30th term,
$a_{30}=a+(30-1) d$
$=4+(29)(5)$
$=4+145$
$=149$
Also, for 10th 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 $a_{30}-a_{10}=100$.
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