How do you write a rule for the nth term of the arithmetic sequence and then find #a_10# for #-4, 2, 8, 14, 20#?

1 Answer
Feb 25, 2017

Answer:

Tenth term #a_10# in given sequence is #50#.

Explanation:

In an arithmetic sequence, the difference between acreen and its immediately preceding term is always constant. This is called as 'common difference'.

Let us check here. Here, we have #2-(-4)=8-2=14-8=20-14=6#.

Hence, here we have an arithmetic sequence with first term #a_1=-4# and common difference #d# equal to #6#.

In an arithmetic sequence if first term is #a_1# and common difference is #d#, then #n(th)# term #a_n# is given by #a_n=a_1+(n-1)d#.

Hence, tenth term in given sequence is

#-4+(10-1)×6=-4+9×6=-4+54=50#.