Two A.P.'s have the same common difference. The first term of one of these is 8 and that of the other is 3. The difference between their 30th term is
(a) 11
(b) 3
(c) 8
(d) 5
Here, we are given two A.P.’s with same common difference. Let us take the common difference as d.
Given,
First term of first A.P. (a) = 8
First term of second A.P. (a’) = 3
We need to find the difference between their 30th terms.
So, let us first find the 30th term of first A.P.
$a_{30}=a+(30-1) d$
$=3+29 d$ $\ldots(1)$
Similarly, we find the 30th term of second A.P.
$a_{30}^{\prime}=a^{\prime}+(30-1) d$
$=3+29 d$ ........(2)
Now, the difference between the $30^{\text {th }}$ terms is,
$a_{30}-a_{30}^{\prime}=(8+29 d)-(3+29 d)$
$=8+29 d-3-29 d$
$=8-3$
$=5$
Therefore, $a_{30}-a_{30}^{\prime}=5$
Hence, the correct option is (d).
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