Question

For what value of c will 2c-7, 5c-9 and 7c+2 be consecutive terms of an arithmetic sequence

Answer 1

$2c-7;\ 5c-9;\ 7c+2-the\ arithmetic\ sequence\ then\\\\(2c-7)+(7c+2)=2\cdot(5c-9)\\\\2c-7+7c+2=10c-18\\\\9c-5=10c-18\ \ \ /+5\ \ /-10c\\\\9c-10c=-18+5\\\\-c=-13\to c=13-answer$



$a_1;\ a_2;\ a_3-the\ arithmetic\ sequence\\\\a_2=a_1+r\\\\a_3=a_2+r=a_1+r+r=a_1+2r\\\\a_1+a_3=a_1+a_1+2r=2a_1+2r=2(a_1+r)=2a_2\\\\\underline{a_1+a_3=2a_2}$