Answer:
1. 15 - RULE : [tex]a_n=a_1+(n-1)d[/tex]
2. 25 - RULE : [tex]a_n=n^{2}[/tex]
3. [tex]\frac{1}{6}[/tex] - RULE : [tex]a_n=\frac{1}{1+(n-1)}[/tex]
4. 29 - RULE : [tex]a_n=\frac{n(n-1)}{2} +1[/tex]
5. -5 - RULE : [tex]a_n=a_1+(n-1)d[/tex]
Step-by-step explanation:
If you want me to explain just comment. So I can edit. Thanks.
[tex]a_n[/tex] = the nᵗʰ term in the sequence
[tex]a_1[/tex] = the first term in the sequence
[tex]d[/tex] = the common difference between terms
[tex]r[/tex] = the common ratio between terms
1.
3, 6, 9, 12, __ (Apply the rule)
[tex]d=6-3=3\\a_5=a_1+(n-1)d\\a_5=3+(5-1)3\\a_5=3+(4)3\\a_5=15[/tex]
2.
1, 4, 9, 16,__ (Apply the rule)
[tex]a_n=n^{2}\\a_5=5^{2}\\a_5=25[/tex]
3.
1, 1/2, 1/3, 1/4, 1/5, __ (Apply the rule)
[tex]a_n=\frac{1}{1+(n-1)}\\a_6=\frac{1}{1+(6-1)}\\a_6=\frac{1}{1+(5)}\\a_n=\frac{1}{6}[/tex]
4.
1, 2, 4, 7, 11, 16, 22,__ (Apply the rule)
[tex]a_n=\frac{n(n-1)}{2} +1\\a_8=\frac{8(8-1)}{2} +1\\a_8=\frac{8(7)}{2} +1\\a_8=\frac{56}{2} +1\\a_8=28 +1\\a_8=29[/tex]
5.
3, 1, -1, -3,__ (Apply the rule)
[tex]d = 1-3=-2\\a_n=a_1+(n-1)d\\a_5=3+(5-1)-2\\a_5=3+(4)-2\\a_5=3+-8\\a_5=-5\\[/tex]
