How do you write a rule for the nth term of the arithmetic sequence given a_10=8, a_16=32?

1 Answer
Aug 5, 2016

{(a_0=-32),(a_(i+1)=a_i+4):}

Explanation:

For an arithmetic sequence < a_0, a_1, a_2, a_3, ... >
terms are related by the formula:
color(white)("XXX")a_m=a_n + (m-n) * k for some constant k

In this example:
color(white)("XXX")a_16=a_10+(16-10) * k
or (using the given values)
color(white)("XXX")32=8+6 * k

color(white)("XX")rarrk=4

And the initial value, a_0 is
color(white)("XXX")a_0 = a_10+(0-10) * k
or
color(white)("XXX")a_0 = 8 +(-10) * (4) = -32

If your standard is to use a_1 as an initial value:
color(white)("XXX")a_1=a_10+(1-10) * k
color(white)("XXXXX") = 8 +(-9) * (4) = -28