Question

1-find the next four terms of an arithmetic sequence 9,16,23.....
2-determine the first 3 terms of the arithmetic progression of which the 5th term is (7+9x) and d=2x

Answer 1

1) $a_1=9,\;\; a_2=16,\;\;a_3=23,\;\;d=16-9=7.$

$a_4=23+7=30,$

$a_5=30+7=37.\\ a_6=37+7=44,\\ a_7=44+7=51.$

2)

$a_5=a_1+4d,\\ a_1=a_5-4d=7+9x-2x*4=7+x,\\ a_2=a_1+d=7+x+2x=7+3x,\\ a_3=a_2+d=7+3x+2x=7+5x.$