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If the pth term of an Ap is q and qth term is p.Prove that it\'s nth term is(p+q-n) |
| Answer» Let the pth term be (a + (p-1)*d) [where d is the common difference and a is the first term of the arithmetic progression].Similarly, the qth term will be (a + (q-1)*d) Now, using the given information:a + (p - 1)*d = q ....(1)a + (q - 1)*d = p ....(2)Substracting (2) from (1), we get d = -1Adding (1) and (2) and putting d = -1, we geta = p + q - 1As above, the nth term will be (a + (n-1)*d)Substituting the values of a and d in this, we getp + q - 1 + (n - 1)*(-1)= p + q - 1 - n + 1= p + q - nHence, we get that the nth term of the series is (p + q - n). | |