Question

Th The sum of the 3rd and 6 terms of an arithmetic sequence is 115 and the 11th term is 77. Find the first term of the sequence.

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Answer 1

Hi,

First term is 12.

Explanation:

I suppose you mean the 6th term.

Let's say a the first term and r the commun difference.

`a_3=a+2*r\\a_6=a+5*r\\a_3+a_6=2a+7*r=115\\a_(11)=a+10*r=77\\\\\left\{\begin{array}{ccc}2a+7r&=&115\ (1)\\a+10r&=&77\ (2) \\\end {array} \right.\\\\\\\left\{\begin{array}{ccc}6r&=&39\ (1)-2*(2) \\a+10r&=&77\\\end {array} \right.\\\\\\\left\{\begin{array}{ccc}r&=&(13)/(2) \\\\a&=&77-10*(13)/(2) \\\end {array} \right.\\\\\\\left\{\begin{array}{ccc}r&=&(13)/(2) \\\\a&=&12 \\\end {array} \right.\\\\`