What is the 21st term of an arithmetic sequence with terms #a_6=50# and #a_11=85#?

1 Answer
Mar 13, 2017

Answer:

#21^(st)# term of the arithmetic sequence is #155#

Explanation:

If #m^(th)# term of an arithmetic series is #a_m# and #n^(th)# term of same series is #a_n#, then common difference is given by

#(a_m-a_n)/(m-n)#

As #a_6=50# and #a_11=85#

#d=(85-50)/(11-6)=35/5=7#

and as #a_6=a_1+(6-1)d#

we have #50=a_1+5xx7#

or #a_1=50-35=15#

and #a_21=a_1+(21-1)d#

#=15+20xx7=15+140=155#