Maluisab45idn
Answered

IDNStudy.com, ang iyong platform ng sanggunian para sa eksaktong mga sagot. Sumali sa aming platform upang makatanggap ng mabilis at eksaktong tugon mula sa mga propesyonal sa iba't ibang larangan.

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]