How do you find the formula for a_n for the arithmetic sequence a_1=x, d=2x?

Feb 22, 2017

${a}_{n} = \left(2 n - 1\right) x$

Explanation:

${n}^{t h}$ term ${a}_{n}$ of an arithmetic sequence, whose first term is ${a}_{1}$ and common difference is $d$ is given by

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

Here ${a}_{1} = x$ and $d = 2 x$, therefore ${a}_{n}$ is given by

${a}_{n} = x + \left(n - 1\right) 2 x = x + \left(2 n - 2\right) x = \left(1 + 2 n - 2\right) x = \left(2 n - 1\right) x$