Question

If the $$5^{th}$$ term of an A.P. is $$31$$ and $$25^{th}$$ term is $$140$$ more than the $$5^{th}$$ term, then find the A.P.

Solution

General $$n^{th}$$ term in AP, $$a_n=a+(n-1)d$$$$a=$$ first term, $$d=$$ common difference.Given, $$a_5=31$$$$\Rightarrow a+4d=31$$ and $$a_{25}=140+a_5$$$$\Rightarrow a+24d=140+a+4d$$$$\Rightarrow 20d=140$$$$\Rightarrow d=7$$$$\Rightarrow a=3$$$$\Rightarrow A.P=3, 10, 17, 24$$,....Maths

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