The second and ninth terms of an arithmetic sequence are 2 and 30, respectively. What is the fiftieth term?
3 Answers
Explanation:
Ok let's say:
This is a characteristic of an arithmetic sequence, each term is separated by a common difference:
In this case:
So, the 5th term:
Explanation:
The nth term of an arithmetic sequence is given by:
Where:
We have:
and
We need to find
Solving
Subtract
Substituting in
So our general term is:
50th term will therefore be:
Explanation:
#"the n th term of an arithmetic sequence is"#
#•color(white)(x)a_n=a+(n-1)d#
#" where a is the first term and d the common difference"#
#a_2=a+d=2to(1)#
#a_9=a+8d=30 to(2)#
#(2)-(1)" gives"#
#7d=28rArrd=4#
#"substitute in "(1)a+4=2rArra=-4#
#rArra_(50)=-2+(49xx4)=-2+196=194#