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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 $$a_{25}=140+a_5$$
$$\Rightarrow a+24d=140+a+4d$$
$$\Rightarrow 20d=140$$
$$\Rightarrow d=7$$
$$\Rightarrow a=3$$
$$\Rightarrow A.P=3, 10, 17, 24$$,....

1216080_1396846_ans_bd69b1472d0643248a4a1c1efa279173.jpg

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