What is the common difference, d, in the arithmetic sequence defined by the formula a_n=-1/2n+6?

Jan 27, 2017

$d = - \frac{1}{2}$.

Explanation:

In any A.P., let us note that, ${T}_{n + 1} - {T}_{n} = d \ldots \left[{T}_{n} \text{ is "n^(th)" term}\right]$.

$\therefore \text{In our Example, } d = {a}_{n + 1} - {a}_{n} = \left\{- \frac{1}{2} \left(n + 1\right) + 6\right\} - \left\{- \frac{1}{2} n + 6\right\} = - \frac{1}{2.}$

There is still a short-cut.

In the Usual Notation,

${T}_{n} = a + \left(n - 1\right) d = \mathrm{dn} + \left(a - d\right) = \mathrm{dn} + b , \text{ say, } b = a - d$

So, $d = \text{the co-eff. of } n \Rightarrow d = - \frac{1}{2.}$