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

Answer:

#{(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#