Question

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

Answer 1

`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`