Question

Use the arithmetic sequence of numbers 1, 3, 5, 7, 9,.to find the following:

Answer 1

$a)\\\\ a_{n+1}-a_n=d\\ for\ n=1\\ a_2-a_1=d\\ d=3-1=2\ - difference\ between\ two\ consecutive\ terms\\\\ b)\\ a_n=a_1+(n-1)d\\ n=101\\ a_{101}=1+(101-1)*2\\ a_{101}=1+100*2=200+1=201\\\\ c)\\ Sn=\frac{a_1+a_n}{2}*n\\ n=20\\ a_n=a_{20}=1+(20-1)*2=1+38=39\\ Sn=\frac{1+39}{2}*20=400\ \ Sum\ of\ the\ first\ 20 \ numbers.$