Question

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

Answer 1

`d=-1/2`.

Explanation:

In any A.P., let us note that, `T_(n+1)-T_n=d...[T_n" is "n^(th)" term"]`.

`:."In our Example, "d=a_(n+1)-a_n={-1/2(n+1)+6}-{-1/2n+6}=-1/2.`

There is still a short-cut.

In the Usual Notation,

`T_n=a+(n-1)d=dn+(a-d)=dn+b," say, "b=a-d`

So, `d="the co-eff. of "n rArr d=-1/2.`