They will be looking for you to derive an equation that gives the value of any term
Let the term count be ii
Let the ith term be a_iai
Let the last term be a_nan
color(brown)("Test for arithmetic sequence:")Test for arithmetic sequence:
12-3=912−3=9
48-12 = 2648−12=26
9!=129≠12 so this is not an arithmetic sequence. Thus is could be a geometric one.
color(brown)("Test for geometric sequence:")Test for geometric sequence:
12-:3=412÷3=4
48-:12=448÷12=4
192-:48=4192÷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=12i=1→a1=3×41=12
i=2->a_2=3xx4^2=3xx16= 48i=2→a2=3×42=3×16=48
i=3->a_3=3xx4^3=3xx64=192i=3→a3=3×43=3×64=192
This works so we have: for any ncolor(white)(" ")a_n=3xx4^nn an=3×4n
Thus at n=7" we have "a_7=3xx4^7 = 49152n=7 we have a7=3×47=49152
