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

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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 = 8 + 29 d ...........(1) Similarly, we find the 30th term of second A.P. a'_(30) = a '+ ( 30 -1) d = 3 + 29 d ...............(2) Now, the difference between the 30th terms is, `a_30 - a'_(30) = (8 + 29d) - ( 3 + 29 d) ` = 8 + 29 d - 3 - 29 d = 8 -3 = 5 Therefore, a_30 - a'_(30) = 5

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