Question

In an A.P, 7th term is 12 and 12th is 72, then find A.P

Answer 1

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Answer 2

$\bf Given:\ \sf The\ 7^{th}\ term\ of\ an\ A.P.\ is\ 12\ and\ the\ 12^{th}\ term\ is\ 72.\\\\\bf To\ find:\ \sf The\ A.P.\\\\\bf Answer: \\\\\sf a_7\ \ =\ 12\ \ \ \ \ \ \ \ \bigg(Equation\ 1. \bigg)\\\\a_1_2\ =\ 72\ \ \ \ \ \ \ \ \bigg(Equation\ 2. \bigg)\\\\\\Equation\ 1\ \implies\ a\ +\ 6d\ =\ 12\\\\Equation\ 2\ \implies\ a\ +\ 11d\ =\ 72\\\\On\ solving,\ we\ get\ d\ (common\ difference)\ =\ 12.\\\\\\\sf Using\ this\ value\ in\ Equation\ 1,\\\\\sf a\ +\ 6\ \times\ \sf 12\ =\ 12$

$\sf a\ +\ 72\ =\ 12\\\\a\ =\ 12\ -\ 72\\\\a\ =\ -60\\\\\\We\ now\ have\ the\ first\ term\ and\ the\ common\ difference.\\\\Therefore, the\ A.P.\ is\ -60, -48, -36, -24, ...\ .$