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.​

Answer 1

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&=&(-9)/(2)*r\\-9r+5r&=&24\end{array}\right.\\\\\\\left\{\begin{array}{ccc}r&=&-6\\a&=&27\end{array}\right.\\\\`