The sum of the first six terms of an A.P is 72 and second term is seven times the fifth term. find the first term and common difference.​

Question

The sum of the first six terms of an A.P is 72 and second term is seven times the fifth term. find the first term and common difference.​

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Farah 3 years 2021-08-01T01:59:06+00:00 1 Answers 45 views 0

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  1. Philomena
    0
    2021-08-01T02:00:35+00:00
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    Hello,

    if A.P means arithmetic progression then

    let’s say a the first term and r the common difference.

    \left\{\begin{array}{ccc}(a)+(a+r)+(a+2r)+...+(a+5r)&=&72\\a+r&=&7*(a+4r)\end{array}\right.\\\\\\\left\{\begin{array}{ccc}6a+15r&=&72\\6a+27r&=&0\end{array}\right.\\\\\\\left\{\begin{array}{ccc}a&=&\dfrac{-9}{2}*r\\-9r+5r&=&24\end{array}\right.\\\\\\\left\{\begin{array}{ccc}r&=&-6\\a&=&27\end{array}\right.\\\\

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