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Question:

Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73.

Solution:

Given that,a11=38a16=73We know that,an=a+(n−1;)da11=a+(11−1;)d38=a+10d... (i)Similarly,a16=a+(16−1;)d73=a+15d... (ii)On subtracting (i) from (ii), we get35=5d∴d=7From equation (i),38=a+(10)(7)⇒38−70=a∴a=−32Nowa31=a+(31−1;)d=−32+30(7)=−32+210=178Hence,31stterm is178.