Question

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

a) What is d, the difference between any two consecutive terms?
b) Using the formula for the nth term of an arithmetic sequence, what is 101st term?
c) Using the formula for the sum of an arithmetic sequence, what is the sum of the first 20 terms?

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=(a_1+a_n)/(2)*n\\ n=20\\ a_n=a_(20)=1+(20-1)*2=1+38=39\\ Sn=(1+39)/(2)*20=400\ \ Sum\ of\ the\ first\ 20 \ numbers.`