SA3 marksYear: 2023MediumCBSE Class 10
arithmetic-progressionsnth-termproof
Question
If pth term of an A.P. is q and qth term is p, then prove that its nth term is (p+q−n).
Solution
1
ap=a+(p−1)d=q ... (i)
+0.5 marks2
aq=a+(q−1)d=p ... (ii)
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Solving (i) and (ii): d=−1, a=q+p−1
+1 mark4
an=(q+p−1)+(n−1)(−1)=q+p−n
+1 mark