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

Mar 13, 2017

${21}^{s t}$ term of the arithmetic sequence is $155$

#### Explanation:

If ${m}^{t h}$ term of an arithmetic series is ${a}_{m}$ and ${n}^{t h}$ term of same series is ${a}_{n}$, then common difference is given by

$\frac{{a}_{m} - {a}_{n}}{m - n}$

As ${a}_{6} = 50$ and ${a}_{11} = 85$

$d = \frac{85 - 50}{11 - 6} = \frac{35}{5} = 7$

and as ${a}_{6} = {a}_{1} + \left(6 - 1\right) d$

we have $50 = {a}_{1} + 5 \times 7$

or ${a}_{1} = 50 - 35 = 15$

and ${a}_{21} = {a}_{1} + \left(21 - 1\right) d$

$= 15 + 20 \times 7 = 15 + 140 = 155$