Maluisab45idn
Answered

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study the pattern and give the next number in each sequence. Then write the rule in finding the nth term on the space provided

1.) 3, 6, 9, 12,___-rule:_____
2.) 1, 4, 9, 16,___-rule:_____
3.) 1/2, 1/3, 1/4, 1/5,___-rule:____
4.) 1, 2, 4, 7, 11, 16, 22,___-rule:____
5.) 3, 1, -1, -3,___-rule:____

Sagot :

Kuleggsidn

1. 15

Rule: 3n

2. 25

Rule: n^2

3. 1/6

Rule: 1/(n+1)

4. 29

Rule: 2^(n-1)

5. -5

Rule: -2n+5

Jackdaniel012998idn

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]

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