Formula for the term of a geometric sequences has been defined as,
"Each number is 4 less than 3 times the previous numbers"
Therefore, recursive formula will be,
[tex]T_n=3(T_{n-1})-4[/tex]
Now we will use this formula to build the sequence,
A). If [tex]T_1=10[/tex],
Then [tex]T_2=3(10)-4=26[/tex]
[tex]T_3=3(26)-4=74[/tex]
[tex]T_4=3(74)-4=218[/tex]
[tex]T_5=3(218)-4=650[/tex]
Therefore, the sequence will be,
[tex]10,26,74,218,650[/tex]
B). If [tex]T_1=1[/tex],
Then [tex]T_2=3(1)-4=-1[/tex]
[tex]T_3=3(-1)-4=-7[/tex]
[tex]T_4=3(-7)-4=-25[/tex]
[tex]T_5=3(-25)-4=-79[/tex]
Therefore, the sequence will be,
[tex]1,-1,-7,-25,-79[/tex]
C). If, [tex]T_1=5[/tex],
Then, [tex]T_2=3(5)-4=11[/tex]
[tex]T_3=3(11)-4=29[/tex]
[tex]T_4=3(29)-4=83[/tex]
[tex]T_5=3(83)-4=245[/tex]
Therefore, the sequence will be,
[tex]5,11,29,83,245[/tex]
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