Question #9a098

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Answer 1 · 2017-02-15T17:35:52

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

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 $n=7" we have "a_7=3xx4^7 = 49152$