Question #9a098

1 Answer
Feb 15, 2017

Answer:

Thus at #n=7" we have "a_7=3xx4^7 = 49152#

Explanation:

They will be looking for you to derive an equation that gives the value of any term

Let the term count be #i#
Let the ith term be #a_i#
Let the last term be #a_n#

#color(brown)("Test for arithmetic sequence:")#
#12-3=9#
#48-12 = 26#

#9!=12# so this is not an arithmetic sequence. Thus is could be a geometric one.

#color(brown)("Test for geometric sequence:")#

#12-:3=4#
#48-:12=4#
#192-:48=4#

The values are all the same so this is a geometric sequence that involves 4 raise to some power

Try:

#i=1->a_1=3xx4^1=12#
#i=2->a_2=3xx4^2=3xx16= 48#
#i=3->a_3=3xx4^3=3xx64=192#

This works so we have: for any # ncolor(white)(" ")a_n=3xx4^n#

Thus at #n=7" we have "a_7=3xx4^7 = 49152#